Cálculo Ejemplos

$y = x {(5 - x)}^{2}$ , $y = x + 2$

Paso 1

Para obtener el volumen del sólido, primero define el área de cada parte, luego integra en el rango. El área de cada parte es el área de un círculo con radio $f (x)$ y $A = π r^{2}$ .

$V = π \int_{0.08641814}^{3.76243349} {(f (x))}^{2} - {(g (x))}^{2} d x$ donde $f (x) = x^{3} - 10 x^{2} + 25 x$ y $g (x) = x + 2$

Paso 2

Simplifica el integrando.

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Paso 2.1

Simplifica cada término.

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Paso 2.1.1

Reescribe ${(x^{3} - 10 x^{2} + 25 x)}^{2}$ como $(x^{3} - 10 x^{2} + 25 x) (x^{3} - 10 x^{2} + 25 x)$ .

$V = (x^{3} - 10 x^{2} + 25 x) (x^{3} - 10 x^{2} + 25 x) - {(x + 2)}^{2}$

Paso 2.1.2

Expande $(x^{3} - 10 x^{2} + 25 x) (x^{3} - 10 x^{2} + 25 x)$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

$V = x^{3} x^{3} + x^{3} (- 10 x^{2}) + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3

Simplifica cada término.

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Paso 2.1.3.1

Multiplica $x^{3}$ por $x^{3}$ sumando los exponentes.

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Paso 2.1.3.1.1

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{3 + 3} + x^{3} (- 10 x^{2}) + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.1.2

Suma $3$ y $3$ .

$V = x^{6} + x^{3} (- 10 x^{2}) + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.2

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{3} x^{2} + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.3

Multiplica $x^{3}$ por $x^{2}$ sumando los exponentes.

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Paso 2.1.3.3.1

Mueve $x^{2}$ .

$V = x^{6} - 10 (x^{2} x^{3}) + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.3.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{2 + 3} + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.3.3

Suma $2$ y $3$ .

$V = x^{6} - 10 x^{5} + x^{3} (25 x) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.4

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{5} + 25 x^{3} x - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.5

Multiplica $x^{3}$ por $x$ sumando los exponentes.

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Paso 2.1.3.5.1

Mueve $x$ .

$V = x^{6} - 10 x^{5} + 25 (x \cdot x^{3}) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.5.2

Multiplica $x$ por $x^{3}$ .

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Paso 2.1.3.5.2.1

Eleva $x$ a la potencia de $1$ .

$V = x^{6} - 10 x^{5} + 25 (x \cdot x^{3}) - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.5.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{1 + 3} - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.5.3

Suma $1$ y $3$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{2} x^{3} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.6

Multiplica $x^{2}$ por $x^{3}$ sumando los exponentes.

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Paso 2.1.3.6.1

Mueve $x^{3}$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 (x^{3} x^{2}) - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.6.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{3 + 2} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.6.3

Suma $3$ y $2$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} - 10 x^{2} (- 10 x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.7

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} - 10 \cdot (- 10 x^{2} x^{2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.8

Multiplica $x^{2}$ por $x^{2}$ sumando los exponentes.

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Paso 2.1.3.8.1

Mueve $x^{2}$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} - 10 \cdot (- 10 (x^{2} x^{2})) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.8.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} - 10 \cdot (- 10 x^{2 + 2}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.8.3

Suma $2$ y $2$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} - 10 \cdot (- 10 x^{4}) - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.9

Multiplica $- 10$ por $- 10$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 x^{2} (25 x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.10

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 \cdot (25 x^{2} x) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.11

Multiplica $x^{2}$ por $x$ sumando los exponentes.

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Paso 2.1.3.11.1

Mueve $x$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 \cdot (25 (x \cdot x^{2})) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.11.2

Multiplica $x$ por $x^{2}$ .

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Paso 2.1.3.11.2.1

Eleva $x$ a la potencia de $1$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 \cdot (25 (x \cdot x^{2})) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.11.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 \cdot (25 x^{1 + 2}) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.11.3

Suma $1$ y $2$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 10 \cdot (25 x^{3}) + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.12

Multiplica $- 10$ por $25$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x \cdot x^{3} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.13

Multiplica $x$ por $x^{3}$ sumando los exponentes.

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Paso 2.1.3.13.1

Mueve $x^{3}$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 (x^{3} x) + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.13.2

Multiplica $x^{3}$ por $x$ .

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Paso 2.1.3.13.2.1

Eleva $x$ a la potencia de $1$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 (x^{3} x) + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.13.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{3 + 1} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.13.3

Suma $3$ y $1$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 x (- 10 x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.14

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 \cdot (- 10 x \cdot x^{2}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.15

Multiplica $x$ por $x^{2}$ sumando los exponentes.

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Paso 2.1.3.15.1

Mueve $x^{2}$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 \cdot (- 10 (x^{2} x)) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.15.2

Multiplica $x^{2}$ por $x$ .

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Paso 2.1.3.15.2.1

Eleva $x$ a la potencia de $1$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 \cdot (- 10 (x^{2} x)) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.15.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 \cdot (- 10 x^{2 + 1}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.15.3

Suma $2$ y $1$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} + 25 \cdot (- 10 x^{3}) + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.16

Multiplica $25$ por $- 10$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 25 x (25 x) - {(x + 2)}^{2}$

Paso 2.1.3.17

Reescribe con la propiedad conmutativa de la multiplicación.

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 25 \cdot (25 x \cdot x) - {(x + 2)}^{2}$

Paso 2.1.3.18

Multiplica $x$ por $x$ sumando los exponentes.

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Paso 2.1.3.18.1

Mueve $x$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 25 \cdot (25 (x \cdot x)) - {(x + 2)}^{2}$

Paso 2.1.3.18.2

Multiplica $x$ por $x$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 25 \cdot (25 x^{2}) - {(x + 2)}^{2}$

Paso 2.1.3.19

Multiplica $25$ por $25$ .

$V = x^{6} - 10 x^{5} + 25 x^{4} - 10 x^{5} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 625 x^{2} - {(x + 2)}^{2}$

Paso 2.1.4

Resta $10 x^{5}$ de $- 10 x^{5}$ .

$V = x^{6} - 20 x^{5} + 25 x^{4} + 100 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 625 x^{2} - {(x + 2)}^{2}$

Paso 2.1.5

Suma $25 x^{4}$ y $100 x^{4}$ .

$V = x^{6} - 20 x^{5} + 125 x^{4} - 250 x^{3} + 25 x^{4} - 250 x^{3} + 625 x^{2} - {(x + 2)}^{2}$

Paso 2.1.6

Suma $125 x^{4}$ y $25 x^{4}$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 250 x^{3} - 250 x^{3} + 625 x^{2} - {(x + 2)}^{2}$

Paso 2.1.7

Resta $250 x^{3}$ de $- 250 x^{3}$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - {(x + 2)}^{2}$

Paso 2.1.8

Reescribe ${(x + 2)}^{2}$ como $(x + 2) (x + 2)$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - ((x + 2) (x + 2))$

Paso 2.1.9

Expande $(x + 2) (x + 2)$ con el método PEIU (primero, exterior, interior, ultimo).

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Paso 2.1.9.1

Aplica la propiedad distributiva.

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x (x + 2) + 2 (x + 2))$

Paso 2.1.9.2

Aplica la propiedad distributiva.

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x \cdot x + x \cdot 2 + 2 (x + 2))$

Paso 2.1.9.3

Aplica la propiedad distributiva.

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2)$

Paso 2.1.10

Simplifica y combina los términos similares.

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Paso 2.1.10.1

Simplifica cada término.

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Paso 2.1.10.1.1

Multiplica $x$ por $x$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2)$

Paso 2.1.10.1.2

Mueve $2$ a la izquierda de $x$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2)$

Paso 2.1.10.1.3

Multiplica $2$ por $2$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x^{2} + 2 x + 2 x + 4)$

Paso 2.1.10.2

Suma $2 x$ y $2 x$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - (x^{2} + 4 x + 4)$

Paso 2.1.11

Aplica la propiedad distributiva.

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - x^{2} - (4 x) - 1 \cdot 4$

Paso 2.1.12

Simplifica.

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Paso 2.1.12.1

Multiplica $4$ por $- 1$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - x^{2} - 4 x - 1 \cdot 4$

Paso 2.1.12.2

Multiplica $- 1$ por $4$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 625 x^{2} - x^{2} - 4 x - 4$

Paso 2.2

Resta $x^{2}$ de $625 x^{2}$ .

$V = x^{6} - 20 x^{5} + 150 x^{4} - 500 x^{3} + 624 x^{2} - 4 x - 4$

Paso 3

Divide la única integral en varias integrales.

$V = π (\int_{0.08641814}^{3.76243349} x^{6} d x + \int_{0.08641814}^{3.76243349} - 20 x^{5} d x + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 4

Según la regla de la potencia, la integral de $x^{6}$ con respecto a $x$ es $\frac{1}{7} x^{7}$ .

$V = π (\frac{1}{7} x^{7}]_{0.08641814}^{3.76243349} + \int_{0.08641814}^{3.76243349} - 20 x^{5} d x + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 5

Combina $\frac{1}{7}$ y $x^{7}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} + \int_{0.08641814}^{3.76243349} - 20 x^{5} d x + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 6

Dado que $- 20$ es constante con respecto a $x$ , mueve $- 20$ fuera de la integral.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 \int_{0.08641814}^{3.76243349} x^{5} d x + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 7

Según la regla de la potencia, la integral de $x^{5}$ con respecto a $x$ es $\frac{1}{6} x^{6}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{1}{6} x^{6}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 8

Combina $\frac{1}{6}$ y $x^{6}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} 150 x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 9

Dado que $150$ es constante con respecto a $x$ , mueve $150$ fuera de la integral.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 \int_{0.08641814}^{3.76243349} x^{4} d x + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 10

Según la regla de la potencia, la integral de $x^{4}$ con respecto a $x$ es $\frac{1}{5} x^{5}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{1}{5} x^{5}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 11

Combina $\frac{1}{5}$ y $x^{5}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 500 x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 12

Dado que $- 500$ es constante con respecto a $x$ , mueve $- 500$ fuera de la integral.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 \int_{0.08641814}^{3.76243349} x^{3} d x + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 13

Según la regla de la potencia, la integral de $x^{3}$ con respecto a $x$ es $\frac{1}{4} x^{4}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{1}{4} x^{4}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 14

Combina $\frac{1}{4}$ y $x^{4}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} 624 x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 15

Dado que $624$ es constante con respecto a $x$ , mueve $624$ fuera de la integral.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 \int_{0.08641814}^{3.76243349} x^{2} d x + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 16

Según la regla de la potencia, la integral de $x^{2}$ con respecto a $x$ es $\frac{1}{3} x^{3}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{1}{3} x^{3}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 17

Combina $\frac{1}{3}$ y $x^{3}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 4 x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 18

Dado que $- 4$ es constante con respecto a $x$ , mueve $- 4$ fuera de la integral.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 \int_{0.08641814}^{3.76243349} x d x + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 19

Según la regla de la potencia, la integral de $x$ con respecto a $x$ es $\frac{1}{2} x^{2}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{1}{2} x^{2}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 20

Combina $\frac{1}{2}$ y $x^{2}$ .

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}) + \int_{0.08641814}^{3.76243349} - 4 d x)$

Paso 21

Aplica la regla de la constante.

$V = π (\frac{x^{7}}{7}]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}) + - 4 x]_{0.08641814}^{3.76243349})$

Paso 22

Simplifica la respuesta.

Toca para ver más pasos...

Paso 22.1

Combina $\frac{x^{7}}{7}]_{0.08641814}^{3.76243349}$ y $- 4 x]_{0.08641814}^{3.76243349}$ .

$V = π (\frac{x^{7}}{7} - 4 x]_{0.08641814}^{3.76243349} - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2

Sustituye y simplifica.

Toca para ver más pasos...

Paso 22.2.1

Evalúa $\frac{x^{7}}{7} - 4 x$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{x^{6}}{6}]_{0.08641814}^{3.76243349}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2.2

Evalúa $\frac{x^{6}}{6}$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 ((\frac{{3.76243349}^{6}}{6}) - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{x^{5}}{5}]_{0.08641814}^{3.76243349}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2.3

Evalúa $\frac{x^{5}}{5}$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{x^{4}}{4}]_{0.08641814}^{3.76243349}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2.4

Evalúa $\frac{x^{4}}{4}$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 ((\frac{{3.76243349}^{4}}{4}) - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{x^{3}}{3}]_{0.08641814}^{3.76243349}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2.5

Evalúa $\frac{x^{3}}{3}$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 (\frac{x^{2}}{2}]_{0.08641814}^{3.76243349}))$

Paso 22.2.6

Evalúa $\frac{x^{2}}{2}$ en $3.76243349$ y en $0.08641814$ .

$V = π ((\frac{{3.76243349}^{7}}{7} - 4 \cdot 3.76243349) - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7

Simplifica.

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Paso 22.2.7.1

Eleva $3.76243349$ a la potencia de $7$ .

$V = π (\frac{10672.88483375}{7} - 4 \cdot 3.76243349 - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.2

Multiplica $- 4$ por $3.76243349$ .

$V = π (\frac{10672.88483375}{7} - 15.04973397 - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.3

Para escribir $- 15.04973397$ como una fracción con un denominador común, multiplica por $\frac{7}{7}$ .

$V = π (\frac{10672.88483375}{7} - 15.04973397 \cdot \frac{7}{7} - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.4

Combina $- 15.04973397$ y $\frac{7}{7}$ .

$V = π (\frac{10672.88483375}{7} + \frac{- 15.04973397 \cdot 7}{7} - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.5

Combina los numeradores sobre el denominador común.

$V = π (\frac{10672.88483375 - 15.04973397 \cdot 7}{7} - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.6

Multiplica $- 15.04973397$ por $7$ .

$V = π (\frac{10672.88483375 - 105.34813781}{7} - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.7

Resta $105.34813781$ de $10672.88483375$ .

$V = π (\frac{10567.53669593}{7} - (\frac{{0.08641814}^{7}}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.8

Eleva $0.08641814$ a la potencia de $7$ .

$V = π (\frac{10567.53669593}{7} - (\frac{0.00000003}{7} - 4 \cdot 0.08641814) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.9

Multiplica $- 4$ por $0.08641814$ .

$V = π (\frac{10567.53669593}{7} - (\frac{0.00000003}{7} - 0.34567259) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.10

Para escribir $- 0.34567259$ como una fracción con un denominador común, multiplica por $\frac{7}{7}$ .

$V = π (\frac{10567.53669593}{7} - (\frac{0.00000003}{7} - 0.34567259 \cdot \frac{7}{7}) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.11

Combina $- 0.34567259$ y $\frac{7}{7}$ .

$V = π (\frac{10567.53669593}{7} - (\frac{0.00000003}{7} + \frac{- 0.34567259 \cdot 7}{7}) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.12

Combina los numeradores sobre el denominador común.

$V = π (\frac{10567.53669593}{7} - \frac{0.00000003 - 0.34567259 \cdot 7}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.13

Multiplica $- 0.34567259$ por $7$ .

$V = π (\frac{10567.53669593}{7} - \frac{0.00000003 - 2.41970818}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.14

Resta $2.41970818$ de $0.00000003$ .

$V = π (\frac{10567.53669593}{7} - \frac{- 2.41970814}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.15

Mueve el negativo al frente de la fracción.

$V = π (\frac{10567.53669593}{7} + \frac{2.41970814}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.16

Multiplica $- 1$ por $- 1$ .

$V = π (\frac{10567.53669593}{7} + 1 (\frac{2.41970814}{7}) - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.17

Multiplica $\frac{2.41970814}{7}$ por $1$ .

Paso 22.2.7.18

Combina los numeradores sobre el denominador común.

$V = π (\frac{10567.53669593 + 2.41970814}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.19

Suma $10567.53669593$ y $2.41970814$ .

$V = π (\frac{10569.95640408}{7} - 20 (\frac{{3.76243349}^{6}}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.20

Eleva $3.76243349$ a la potencia de $6$ .

$V = π (\frac{10569.95640408}{7} - 20 (\frac{2836.69727376}{6} - \frac{{0.08641814}^{6}}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.21

Eleva $0.08641814$ a la potencia de $6$ .

$V = π (\frac{10569.95640408}{7} - 20 (\frac{2836.69727376}{6} - \frac{0.00000041}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.22

Combina los numeradores sobre el denominador común.

$V = π (\frac{10569.95640408}{7} - 20 \frac{2836.69727376 - 0.00000041}{6} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.23

Resta $0.00000041$ de $2836.69727376$ .

$V = π (\frac{10569.95640408}{7} - 20 (\frac{2836.69727334}{6}) + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.24

Combina $- 20$ y $\frac{2836.69727334}{6}$ .

$V = π (\frac{10569.95640408}{7} + \frac{- 20 \cdot 2836.69727334}{6} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.25

Multiplica $- 20$ por $2836.69727334$ .

$V = π (\frac{10569.95640408}{7} + \frac{- 56733.94546694}{6} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.26

Mueve el negativo al frente de la fracción.

$V = π (\frac{10569.95640408}{7} - \frac{56733.94546694}{6} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.27

Para escribir $\frac{10569.95640408}{7}$ como una fracción con un denominador común, multiplica por $\frac{6}{6}$ .

$V = π (\frac{10569.95640408}{7} \cdot \frac{6}{6} - \frac{56733.94546694}{6} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.28

Para escribir $- \frac{56733.94546694}{6}$ como una fracción con un denominador común, multiplica por $\frac{7}{7}$ .

$V = π (\frac{10569.95640408}{7} \cdot \frac{6}{6} - \frac{56733.94546694}{6} \cdot \frac{7}{7} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.29

Escribe cada expresión con un denominador común de $42$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

Toca para ver más pasos...

Paso 22.2.7.29.1

Multiplica $\frac{10569.95640408}{7}$ por $\frac{6}{6}$ .

$V = π (\frac{10569.95640408 \cdot 6}{7 \cdot 6} - \frac{56733.94546694}{6} \cdot \frac{7}{7} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.29.2

Multiplica $7$ por $6$ .

$V = π (\frac{10569.95640408 \cdot 6}{42} - \frac{56733.94546694}{6} \cdot \frac{7}{7} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.29.3

Multiplica $\frac{56733.94546694}{6}$ por $\frac{7}{7}$ .

$V = π (\frac{10569.95640408 \cdot 6}{42} - \frac{56733.94546694 \cdot 7}{6 \cdot 7} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.29.4

Multiplica $6$ por $7$ .

$V = π (\frac{10569.95640408 \cdot 6}{42} - \frac{56733.94546694 \cdot 7}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.30

Combina los numeradores sobre el denominador común.

$V = π (\frac{10569.95640408 \cdot 6 - 56733.94546694 \cdot 7}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.31

Multiplica $10569.95640408$ por $6$ .

$V = π (\frac{63419.73842452 - 56733.94546694 \cdot 7}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.32

Multiplica $- 56733.94546694$ por $7$ .

$V = π (\frac{63419.73842452 - 397137.61826859}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.33

Resta $397137.61826859$ de $63419.73842452$ .

$V = π (\frac{- 333717.87984406}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.34

Mueve el negativo al frente de la fracción.

$V = π (- \frac{333717.87984406}{42} + 150 (\frac{{3.76243349}^{5}}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.35

Eleva $3.76243349$ a la potencia de $5$ .

$V = π (- \frac{333717.87984406}{42} + 150 (\frac{753.95280173}{5} - \frac{{0.08641814}^{5}}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.36

Eleva $0.08641814$ a la potencia de $5$ .

$V = π (- \frac{333717.87984406}{42} + 150 (\frac{753.95280173}{5} - \frac{0.00000481}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.37

Combina los numeradores sobre el denominador común.

$V = π (- \frac{333717.87984406}{42} + 150 (\frac{753.95280173 - 0.00000481}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.38

Resta $0.00000481$ de $753.95280173$ .

$V = π (- \frac{333717.87984406}{42} + 150 (\frac{753.95279691}{5}) - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.39

Combina $150$ y $\frac{753.95279691}{5}$ .

$V = π (- \frac{333717.87984406}{42} + \frac{150 \cdot 753.95279691}{5} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.40

Multiplica $150$ por $753.95279691$ .

$V = π (- \frac{333717.87984406}{42} + \frac{113092.91953688}{5} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.41

Para escribir $- \frac{333717.87984406}{42}$ como una fracción con un denominador común, multiplica por $\frac{5}{5}$ .

$V = π (- \frac{333717.87984406}{42} \cdot \frac{5}{5} + \frac{113092.91953688}{5} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.42

Para escribir $\frac{113092.91953688}{5}$ como una fracción con un denominador común, multiplica por $\frac{42}{42}$ .

$V = π (- \frac{333717.87984406}{42} \cdot \frac{5}{5} + \frac{113092.91953688}{5} \cdot \frac{42}{42} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.43

Escribe cada expresión con un denominador común de $210$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

Toca para ver más pasos...

Paso 22.2.7.43.1

Multiplica $\frac{333717.87984406}{42}$ por $\frac{5}{5}$ .

$V = π (- \frac{333717.87984406 \cdot 5}{42 \cdot 5} + \frac{113092.91953688}{5} \cdot \frac{42}{42} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.43.2

Multiplica $42$ por $5$ .

$V = π (- \frac{333717.87984406 \cdot 5}{210} + \frac{113092.91953688}{5} \cdot \frac{42}{42} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.43.3

Multiplica $\frac{113092.91953688}{5}$ por $\frac{42}{42}$ .

$V = π (- \frac{333717.87984406 \cdot 5}{210} + \frac{113092.91953688 \cdot 42}{5 \cdot 42} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.43.4

Multiplica $5$ por $42$ .

$V = π (- \frac{333717.87984406 \cdot 5}{210} + \frac{113092.91953688 \cdot 42}{210} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.44

Combina los numeradores sobre el denominador común.

$V = π (\frac{- 333717.87984406 \cdot 5 + 113092.91953688 \cdot 42}{210} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.45

Multiplica $- 333717.87984406$ por $5$ .

$V = π (\frac{- 1668589.39922034 + 113092.91953688 \cdot 42}{210} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.46

Multiplica $113092.91953688$ por $42$ .

$V = π (\frac{- 1668589.39922034 + 4749902.62054914}{210} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.47

Suma $- 1668589.39922034$ y $4749902.62054914$ .

$V = π (\frac{3081313.22132879}{210} - 500 (\frac{{3.76243349}^{4}}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.48

Eleva $3.76243349$ a la potencia de $4$ .

$V = π (\frac{3081313.22132879}{210} - 500 (\frac{200.38966882}{4} - \frac{{0.08641814}^{4}}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.49

Eleva $0.08641814$ a la potencia de $4$ .

$V = π (\frac{3081313.22132879}{210} - 500 (\frac{200.38966882}{4} - \frac{0.00005577}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.50

Combina los numeradores sobre el denominador común.

$V = π (\frac{3081313.22132879}{210} - 500 \frac{200.38966882 - 0.00005577}{4} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.51

Resta $0.00005577$ de $200.38966882$ .

$V = π (\frac{3081313.22132879}{210} - 500 (\frac{200.38961305}{4}) + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.52

Combina $- 500$ y $\frac{200.38961305}{4}$ .

$V = π (\frac{3081313.22132879}{210} + \frac{- 500 \cdot 200.38961305}{4} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.53

Multiplica $- 500$ por $200.38961305$ .

$V = π (\frac{3081313.22132879}{210} + \frac{- 100194.80652516}{4} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.54

Mueve el negativo al frente de la fracción.

$V = π (\frac{3081313.22132879}{210} - \frac{100194.80652516}{4} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.55

Para escribir $\frac{3081313.22132879}{210}$ como una fracción con un denominador común, multiplica por $\frac{2}{2}$ .

$V = π (\frac{3081313.22132879}{210} \cdot \frac{2}{2} - \frac{100194.80652516}{4} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.56

Para escribir $- \frac{100194.80652516}{4}$ como una fracción con un denominador común, multiplica por $\frac{105}{105}$ .

$V = π (\frac{3081313.22132879}{210} \cdot \frac{2}{2} - \frac{100194.80652516}{4} \cdot \frac{105}{105} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.57

Escribe cada expresión con un denominador común de $420$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

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Paso 22.2.7.57.1

Multiplica $\frac{3081313.22132879}{210}$ por $\frac{2}{2}$ .

$V = π (\frac{3081313.22132879 \cdot 2}{210 \cdot 2} - \frac{100194.80652516}{4} \cdot \frac{105}{105} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.57.2

Multiplica $210$ por $2$ .

$V = π (\frac{3081313.22132879 \cdot 2}{420} - \frac{100194.80652516}{4} \cdot \frac{105}{105} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.57.3

Multiplica $\frac{100194.80652516}{4}$ por $\frac{105}{105}$ .

$V = π (\frac{3081313.22132879 \cdot 2}{420} - \frac{100194.80652516 \cdot 105}{4 \cdot 105} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.57.4

Multiplica $4$ por $105$ .

$V = π (\frac{3081313.22132879 \cdot 2}{420} - \frac{100194.80652516 \cdot 105}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.58

Combina los numeradores sobre el denominador común.

$V = π (\frac{3081313.22132879 \cdot 2 - 100194.80652516 \cdot 105}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.59

Multiplica $3081313.22132879$ por $2$ .

$V = π (\frac{6162626.44265759 - 100194.80652516 \cdot 105}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.60

Multiplica $- 100194.80652516$ por $105$ .

$V = π (\frac{6162626.44265759 - 10520454.6851421}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.61

Resta $10520454.6851421$ de $6162626.44265759$ .

$V = π (\frac{- 4357828.24248451}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.62

Mueve el negativo al frente de la fracción.

$V = π (- \frac{4357828.24248451}{420} + 624 (\frac{{3.76243349}^{3}}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.63

Eleva $3.76243349$ a la potencia de $3$ .

$V = π (- \frac{4357828.24248451}{420} + 624 (\frac{53.26065408}{3} - \frac{{0.08641814}^{3}}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.64

Eleva $0.08641814$ a la potencia de $3$ .

$V = π (- \frac{4357828.24248451}{420} + 624 (\frac{53.26065408}{3} - \frac{0.00064537}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.65

Combina los numeradores sobre el denominador común.

$V = π (- \frac{4357828.24248451}{420} + 624 (\frac{53.26065408 - 0.00064537}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.66

Resta $0.00064537$ de $53.26065408$ .

$V = π (- \frac{4357828.24248451}{420} + 624 (\frac{53.2600087}{3}) - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.67

Combina $624$ y $\frac{53.2600087}{3}$ .

$V = π (- \frac{4357828.24248451}{420} + \frac{624 \cdot 53.2600087}{3} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.68

Multiplica $624$ por $53.2600087$ .

$V = π (- \frac{4357828.24248451}{420} + \frac{33234.24543367}{3} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.69

Para escribir $\frac{33234.24543367}{3}$ como una fracción con un denominador común, multiplica por $\frac{140}{140}$ .

$V = π (- \frac{4357828.24248451}{420} + \frac{33234.24543367}{3} \cdot \frac{140}{140} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.70

Escribe cada expresión con un denominador común de $420$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

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Paso 22.2.7.70.1

Multiplica $\frac{33234.24543367}{3}$ por $\frac{140}{140}$ .

$V = π (- \frac{4357828.24248451}{420} + \frac{33234.24543367 \cdot 140}{3 \cdot 140} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.70.2

Multiplica $3$ por $140$ .

$V = π (- \frac{4357828.24248451}{420} + \frac{33234.24543367 \cdot 140}{420} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.71

Combina los numeradores sobre el denominador común.

$V = π (\frac{- 4357828.24248451 + 33234.24543367 \cdot 140}{420} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.72

Multiplica $33234.24543367$ por $140$ .

$V = π (\frac{- 4357828.24248451 + 4652794.36071416}{420} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.73

Suma $- 4357828.24248451$ y $4652794.36071416$ .

$V = π (\frac{294966.11822965}{420} - 4 ((\frac{{3.76243349}^{2}}{2}) - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.74

Eleva $3.76243349$ a la potencia de $2$ .

$V = π (\frac{294966.11822965}{420} - 4 (\frac{14.15590579}{2} - \frac{{0.08641814}^{2}}{2}))$

Paso 22.2.7.75

Eleva $0.08641814$ a la potencia de $2$ .

$V = π (\frac{294966.11822965}{420} - 4 (\frac{14.15590579}{2} - \frac{0.00746809}{2}))$

Paso 22.2.7.76

Combina los numeradores sobre el denominador común.

$V = π (\frac{294966.11822965}{420} - 4 \frac{14.15590579 - 0.00746809}{2})$

Paso 22.2.7.77

Resta $0.00746809$ de $14.15590579$ .

$V = π (\frac{294966.11822965}{420} - 4 (\frac{14.14843769}{2}))$

Paso 22.2.7.78

Combina $- 4$ y $\frac{14.14843769}{2}$ .

$V = π (\frac{294966.11822965}{420} + \frac{- 4 \cdot 14.14843769}{2})$

Paso 22.2.7.79

Multiplica $- 4$ por $14.14843769$ .

$V = π (\frac{294966.11822965}{420} + \frac{- 56.59375078}{2})$

Paso 22.2.7.80

Mueve el negativo al frente de la fracción.

$V = π (\frac{294966.11822965}{420} - \frac{56.59375078}{2})$

Paso 22.2.7.81

Para escribir $- \frac{56.59375078}{2}$ como una fracción con un denominador común, multiplica por $\frac{210}{210}$ .

$V = π (\frac{294966.11822965}{420} - \frac{56.59375078}{2} \cdot \frac{210}{210})$

Paso 22.2.7.82

Escribe cada expresión con un denominador común de $420$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

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Paso 22.2.7.82.1

Multiplica $\frac{56.59375078}{2}$ por $\frac{210}{210}$ .

$V = π (\frac{294966.11822965}{420} - \frac{56.59375078 \cdot 210}{2 \cdot 210})$

Paso 22.2.7.82.2

Multiplica $2$ por $210$ .

$V = π (\frac{294966.11822965}{420} - \frac{56.59375078 \cdot 210}{420})$

Paso 22.2.7.83

Combina los numeradores sobre el denominador común.

$V = π (\frac{294966.11822965 - 56.59375078 \cdot 210}{420})$

Paso 22.2.7.84

Multiplica $- 56.59375078$ por $210$ .

$V = π (\frac{294966.11822965 - 11884.68766509}{420})$

Paso 22.2.7.85

Resta $11884.68766509$ de $294966.11822965$ .

$V = π (\frac{283081.43056456}{420})$

Paso 22.2.7.86

Combina $π$ y $\frac{283081.43056456}{420}$ .

$V = \frac{π \cdot 283081.43056456}{420}$

Paso 22.2.7.87

Multiplica $π$ por $283081.43056456$ .

$V = \frac{889326.54262932}{420}$

Paso 23

Divide $889326.54262932$ por $420$ .

$V = 2117.44414911$

Paso 24