Cálculo Ejemplos

y = - 7 x^{2} + 21 x

$y = - 7 x^{2} + 21 x$ ,

y = 3 x

$y = 3 x$

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)

$f (x)$ y

A = π r^{2}

$A = π r^{2}$ .

V = π \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} {(f (x))}^{2} - {(g (x))}^{2} d x

$V = π \int_{0}^{2.\overline{571428}} {(f (x))}^{2} - {(g (x))}^{2} d x$ donde

f (x) = - 7 x^{2} + 21 x

$f (x) = - 7 x^{2} + 21 x$ y

g (x) = 3 x

$g (x) = 3 x$

Paso 2

Simplifica el integrando.

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Paso 2.1

Simplifica cada término.

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Paso 2.1.1

Reescribe

{(- 7 x^{2} + 21 x)}^{2}

${(- 7 x^{2} + 21 x)}^{2}$ como

(- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x)

$(- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x)$ .

V = (- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x) - {(3 x)}^{2}

$V = (- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x) - {(3 x)}^{2}$

Paso 2.1.2

Expande

(- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x)

$(- 7 x^{2} + 21 x) (- 7 x^{2} + 21 x)$ con el método PEIU (primero, exterior, interior, ultimo).

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Paso 2.1.2.1

Aplica la propiedad distributiva.

V = - 7 x^{2} (- 7 x^{2} + 21 x) + 21 x (- 7 x^{2} + 21 x) - {(3 x)}^{2}

$V = - 7 x^{2} (- 7 x^{2} + 21 x) + 21 x (- 7 x^{2} + 21 x) - {(3 x)}^{2}$

Paso 2.1.2.2

Aplica la propiedad distributiva.

V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2} + 21 x) - {(3 x)}^{2}

$V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2} + 21 x) - {(3 x)}^{2}$

Paso 2.1.2.3

Aplica la propiedad distributiva.

V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 x^{2} (- 7 x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3

Simplifica y combina los términos similares.

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Paso 2.1.3.1

Simplifica cada término.

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Paso 2.1.3.1.1

Reescribe con la propiedad conmutativa de la multiplicación.

V = - 7 \cdot (- 7 x^{2} x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 \cdot (- 7 x^{2} x^{2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.2

Multiplica

x^{2}

$x^{2}$ por

x^{2}

$x^{2}$ sumando los exponentes.

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Paso 2.1.3.1.2.1

Mueve

x^{2}

$x^{2}$ .

V = - 7 \cdot (- 7 (x^{2} x^{2})) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 \cdot (- 7 (x^{2} x^{2})) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.2.2

Usa la regla de la potencia

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

V = - 7 \cdot (- 7 x^{2 + 2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 \cdot (- 7 x^{2 + 2}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.2.3

Suma

2

$2$ y

2

$2$ .

V = - 7 \cdot (- 7 x^{4}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 \cdot (- 7 x^{4}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

V = - 7 \cdot (- 7 x^{4}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = - 7 \cdot (- 7 x^{4}) - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.3

Multiplica

- 7

$- 7$ por

- 7

$- 7$ .

V = 49 x^{4} - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 x^{2} (21 x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.4

Reescribe con la propiedad conmutativa de la multiplicación.

V = 49 x^{4} - 7 \cdot (21 x^{2} x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 x^{2} x) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.5

Multiplica

x^{2}

$x^{2}$ por

x

$x$ sumando los exponentes.

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Paso 2.1.3.1.5.1

Mueve

x

$x$ .

V = 49 x^{4} - 7 \cdot (21 (x \cdot x^{2})) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 (x \cdot x^{2})) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.5.2

Multiplica

x

$x$ por

x^{2}

$x^{2}$ .

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Paso 2.1.3.1.5.2.1

Eleva

x

$x$ a la potencia de

1

$1$ .

V = 49 x^{4} - 7 \cdot (21 (x \cdot x^{2})) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 (x \cdot x^{2})) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.5.2.2

Usa la regla de la potencia

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

V = 49 x^{4} - 7 \cdot (21 x^{1 + 2}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 x^{1 + 2}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

V = 49 x^{4} - 7 \cdot (21 x^{1 + 2}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 x^{1 + 2}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.5.3

Suma

1

$1$ y

2

$2$ .

V = 49 x^{4} - 7 \cdot (21 x^{3}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 x^{3}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

V = 49 x^{4} - 7 \cdot (21 x^{3}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 7 \cdot (21 x^{3}) + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.6

Multiplica

- 7

$- 7$ por

21

$21$ .

V = 49 x^{4} - 147 x^{3} + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 x (- 7 x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.7

Reescribe con la propiedad conmutativa de la multiplicación.

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x \cdot x^{2}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x \cdot x^{2}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.8

Multiplica

x

$x$ por

x^{2}

$x^{2}$ sumando los exponentes.

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Paso 2.1.3.1.8.1

Mueve

x^{2}

$x^{2}$ .

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 (x^{2} x)) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 (x^{2} x)) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.8.2

Multiplica

x^{2}

$x^{2}$ por

x

$x$ .

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Paso 2.1.3.1.8.2.1

Eleva

x

$x$ a la potencia de

1

$1$ .

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 (x^{2} x)) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 (x^{2} x)) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.8.2.2

Usa la regla de la potencia

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{2 + 1}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{2 + 1}) + 21 x (21 x) - {(3 x)}^{2}$

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{2 + 1}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{2 + 1}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.8.3

Suma

2

$2$ y

1

$1$ .

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{3}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{3}) + 21 x (21 x) - {(3 x)}^{2}$

V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{3}) + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} + 21 \cdot (- 7 x^{3}) + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.9

Multiplica

21

$21$ por

- 7

$- 7$ .

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 x (21 x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 x (21 x) - {(3 x)}^{2}$

Paso 2.1.3.1.10

Reescribe con la propiedad conmutativa de la multiplicación.

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x \cdot x) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x \cdot x) - {(3 x)}^{2}$

Paso 2.1.3.1.11

Multiplica

x

$x$ por

x

$x$ sumando los exponentes.

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Paso 2.1.3.1.11.1

Mueve

x

$x$ .

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 (x \cdot x)) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 (x \cdot x)) - {(3 x)}^{2}$

Paso 2.1.3.1.11.2

Multiplica

x

$x$ por

x

$x$ .

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x^{2}) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x^{2}) - {(3 x)}^{2}$

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x^{2}) - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 21 \cdot (21 x^{2}) - {(3 x)}^{2}$

Paso 2.1.3.1.12

Multiplica

21

$21$ por

21

$21$ .

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 441 x^{2} - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 441 x^{2} - {(3 x)}^{2}$

V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 441 x^{2} - {(3 x)}^{2}

$V = 49 x^{4} - 147 x^{3} - 147 x^{3} + 441 x^{2} - {(3 x)}^{2}$

Paso 2.1.3.2

Resta

147 x^{3}

$147 x^{3}$ de

- 147 x^{3}

$- 147 x^{3}$ .

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - {(3 x)}^{2}

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - {(3 x)}^{2}$

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - {(3 x)}^{2}

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - {(3 x)}^{2}$

Paso 2.1.4

Aplica la regla del producto a

3 x

$3 x$ .

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - (3^{2} x^{2})

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - (3^{2} x^{2})$

Paso 2.1.5

Eleva

3

$3$ a la potencia de

2

$2$ .

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - (9 x^{2})

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - (9 x^{2})$

Paso 2.1.6

Multiplica

9

$9$ por

- 1

$- 1$ .

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - 9 x^{2}

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - 9 x^{2}$

V = 49 x^{4} - 294 x^{3} + 441 x^{2} - 9 x^{2}

$V = 49 x^{4} - 294 x^{3} + 441 x^{2} - 9 x^{2}$

Paso 2.2

Resta

9 x^{2}

$9 x^{2}$ de

441 x^{2}

$441 x^{2}$ .

V = 49 x^{4} - 294 x^{3} + 432 x^{2}

$V = 49 x^{4} - 294 x^{3} + 432 x^{2}$

V = 49 x^{4} - 294 x^{3} + 432 x^{2}

$V = 49 x^{4} - 294 x^{3} + 432 x^{2}$

Paso 3

Divide la única integral en varias integrales.

V = π (\int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 49 x^{4} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} - 294 x^{3} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (\int_{0}^{2.\overline{571428}} 49 x^{4} d x + \int_{0}^{2.\overline{571428}} - 294 x^{3} d x + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 4

Dado que

49

$49$ es constante con respecto a

x

$x$ , mueve

49

$49$ fuera de la integral.

V = π (49 \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} x^{4} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} - 294 x^{3} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 \int_{0}^{2.\overline{571428}} x^{4} d x + \int_{0}^{2.\overline{571428}} - 294 x^{3} d x + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 5

Según la regla de la potencia, la integral de

x^{4}

$x^{4}$ con respecto a

x

$x$ es

\frac{1}{5} x^{5}

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

V = π (49 (\frac{1}{5} x^{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} - 294 x^{3} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 (\frac{1}{5} x^{5}]_{0}^{2.\overline{571428}}) + \int_{0}^{2.\overline{571428}} - 294 x^{3} d x + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 6

Combina

\frac{1}{5}

$\frac{1}{5}$ y

x^{5}

$x^{5}$ .

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} - 294 x^{3} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) + \int_{0}^{2.\overline{571428}} - 294 x^{3} d x + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 7

Dado que

- 294

$- 294$ es constante con respecto a

x

$x$ , mueve

- 294

$- 294$ fuera de la integral.

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} x^{3} d x + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 \int_{0}^{2.\overline{571428}} x^{3} d x + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 8

Según la regla de la potencia, la integral de

x^{3}

$x^{3}$ con respecto a

x

$x$ es

\frac{1}{4} x^{4}

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

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 (\frac{1}{4} x^{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 (\frac{1}{4} x^{4}]_{0}^{2.\overline{571428}}) + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 9

Combina

\frac{1}{4}

$\frac{1}{4}$ y

x^{4}

$x^{4}$ .

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 (\frac{x^{4}}{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} 432 x^{2} d x)

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 (\frac{x^{4}}{4}]_{0}^{2.\overline{571428}}) + \int_{0}^{2.\overline{571428}} 432 x^{2} d x)$

Paso 10

Dado que

432

$432$ es constante con respecto a

x

$x$ , mueve

432

$432$ fuera de la integral.

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 (\frac{x^{4}}{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + 432 \int_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428} x^{2} d x)

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 (\frac{x^{4}}{4}]_{0}^{2.\overline{571428}}) + 432 \int_{0}^{2.\overline{571428}} x^{2} d x)$

Paso 11

Según la regla de la potencia, la integral de

x^{2}

$x^{2}$ con respecto a

x

$x$ es

\frac{1}{3} x^{3}

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

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 (\frac{x^{4}}{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + 432 (\frac{1}{3} x^{3}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}))

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 (\frac{x^{4}}{4}]_{0}^{2.\overline{571428}}) + 432 (\frac{1}{3} x^{3}]_{0}^{2.\overline{571428}}))$

Paso 12

Simplifica la respuesta.

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Paso 12.1

Combina

\frac{1}{3}

$\frac{1}{3}$ y

x^{3}

$x^{3}$ .

V = π (49 (\frac{x^{5}}{5}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) - 294 (\frac{x^{4}}{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + 432 (\frac{x^{3}}{3}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}))

$V = π (49 (\frac{x^{5}}{5}]_{0}^{2.\overline{571428}}) - 294 (\frac{x^{4}}{4}]_{0}^{2.\overline{571428}}) + 432 (\frac{x^{3}}{3}]_{0}^{2.\overline{571428}}))$

Paso 12.2

Sustituye y simplifica.

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Paso 12.2.1

Evalúa

\frac{x^{5}}{5}

$\frac{x^{5}}{5}$ en

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ y en

0

$0$ .

V = π (49 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{5}}{5}) - \frac{0^{5}}{5}) - 294 (\frac{x^{4}}{4}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}) + 432 (\frac{x^{3}}{3}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}))

$V = π (49 ((\frac{{2.\overline{571428}}^{5}}{5}) - \frac{0^{5}}{5}) - 294 (\frac{x^{4}}{4}]_{0}^{2.\overline{571428}}) + 432 (\frac{x^{3}}{3}]_{0}^{2.\overline{571428}}))$

Paso 12.2.2

Evalúa

\frac{x^{4}}{4}

$\frac{x^{4}}{4}$ en

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ y en

0

$0$ .

V = π (49 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{5}}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 (\frac{x^{3}}{3}]_{0}^{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}))

$V = π (49 (\frac{{2.\overline{571428}}^{5}}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 (\frac{x^{3}}{3}]_{0}^{2.\overline{571428}}))$

Paso 12.2.3

Evalúa

\frac{x^{3}}{3}

$\frac{x^{3}}{3}$ en

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ y en

0

$0$ .

V = π (49 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{5}}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{{2.\overline{571428}}^{5}}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4

Simplifica.

Toca para ver más pasos...

Paso 12.2.4.1

Eleva

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ a la potencia de

5

$5$ .

V = π (49 (\frac{112.42744094}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{0^{5}}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.2

Elevar

0

$0$ a cualquier potencia positiva da como resultado

0

$0$ .

V = π (49 (\frac{112.42744094}{5} - \frac{0}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{0}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.3

Cancela el factor común de

0

$0$ y

5

$5$ .

Toca para ver más pasos...

Paso 12.2.4.3.1

Factoriza

5

$5$ de

0

$0$ .

V = π (49 (\frac{112.42744094}{5} - \frac{5 (0)}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{5 (0)}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.3.2

Cancela los factores comunes.

Toca para ver más pasos...

Paso 12.2.4.3.2.1

Factoriza

5

$5$ de

5

$5$ .

V = π (49 (\frac{112.42744094}{5} - \frac{5 \cdot 0}{5 \cdot 1}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{5 \cdot 0}{5 \cdot 1}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.3.2.2

Cancela el factor común.

V = π (49 (\frac{112.42744094}{5} - \frac{5 \cdot 0}{5 \cdot 1}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{5 \cdot 0}{5 \cdot 1}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.3.2.3

Reescribe la expresión.

V = π (49 (\frac{112.42744094}{5} - \frac{0}{1}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - \frac{0}{1}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.3.2.4

Divide

0

$0$ por

1

$1$ .

V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} - 0) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.4

Multiplica

- 1

$- 1$ por

0

$0$ .

V = π (49 (\frac{112.42744094}{5} + 0) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5} + 0) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.5

Suma

\frac{112.42744094}{5}

$\frac{112.42744094}{5}$ y

0

$0$ .

V = π (49 (\frac{112.42744094}{5}) - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (49 (\frac{112.42744094}{5}) - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.6

Combina

49

$49$ y

\frac{112.42744094}{5}

$\frac{112.42744094}{5}$ .

V = π (\frac{49 \cdot 112.42744094}{5} - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{49 \cdot 112.42744094}{5} - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.7

Multiplica

49

$49$ por

112.42744094

$112.42744094$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{{2.\overline{571428}}^{4}}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.8

Eleva

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ a la potencia de

4

$4$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0^{4}}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.9

Elevar

0

$0$ a cualquier potencia positiva da como resultado

0

$0$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.10

Cancela el factor común de

0

$0$ y

4

$4$ .

Toca para ver más pasos...

Paso 12.2.4.10.1

Factoriza

4

$4$ de

0

$0$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 (0)}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 (0)}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.10.2

Cancela los factores comunes.

Toca para ver más pasos...

Paso 12.2.4.10.2.1

Factoriza

4

$4$ de

4

$4$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 \cdot 0}{4 \cdot 1}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 \cdot 0}{4 \cdot 1}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.10.2.2

Cancela el factor común.

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 \cdot 0}{4 \cdot 1}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{4 \cdot 0}{4 \cdot 1}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.10.2.3

Reescribe la expresión.

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0}{1}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - \frac{0}{1}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.10.2.4

Divide

0

$0$ por

1

$1$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} - 0) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.11

Multiplica

- 1

$- 1$ por

0

$0$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} + 0) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4} + 0) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.12

Suma

\frac{43.72178259}{4}

$\frac{43.72178259}{4}$ y

0

$0$ .

V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4}) + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - 294 (\frac{43.72178259}{4}) + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.13

Combina

- 294

$- 294$ y

\frac{43.72178259}{4}

$\frac{43.72178259}{4}$ .

V = π (\frac{5508.94460641}{5} + \frac{- 294 \cdot 43.72178259}{4} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} + \frac{- 294 \cdot 43.72178259}{4} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.14

Multiplica

- 294

$- 294$ por

43.72178259

$43.72178259$ .

V = π (\frac{5508.94460641}{5} + \frac{- 12854.20408163}{4} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} + \frac{- 12854.20408163}{4} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.15

Mueve el negativo al frente de la fracción.

V = π (\frac{5508.94460641}{5} - \frac{12854.20408163}{4} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} - \frac{12854.20408163}{4} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.16

Para escribir

\frac{5508.94460641}{5}

$\frac{5508.94460641}{5}$ como una fracción con un denominador común, multiplica por

\frac{4}{4}

$\frac{4}{4}$ .

V = π (\frac{5508.94460641}{5} \cdot \frac{4}{4} - \frac{12854.20408163}{4} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} \cdot \frac{4}{4} - \frac{12854.20408163}{4} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.17

Para escribir

- \frac{12854.20408163}{4}

$- \frac{12854.20408163}{4}$ como una fracción con un denominador común, multiplica por

\frac{5}{5}

$\frac{5}{5}$ .

V = π (\frac{5508.94460641}{5} \cdot \frac{4}{4} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641}{5} \cdot \frac{4}{4} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.18

Escribe cada expresión con un denominador común de

20

$20$ , mediante la multiplicación de cada uno por un factor adecuado de

1

$1$ .

Toca para ver más pasos...

Paso 12.2.4.18.1

Multiplica

\frac{5508.94460641}{5}

$\frac{5508.94460641}{5}$ por

\frac{4}{4}

$\frac{4}{4}$ .

V = π (\frac{5508.94460641 \cdot 4}{5 \cdot 4} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4}{5 \cdot 4} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.18.2

Multiplica

5

$5$ por

4

$4$ .

V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163}{4} \cdot \frac{5}{5} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.18.3

Multiplica

\frac{12854.20408163}{4}

$\frac{12854.20408163}{4}$ por

\frac{5}{5}

$\frac{5}{5}$ .

V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{4 \cdot 5} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{4 \cdot 5} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.18.4

Multiplica

4

$4$ por

5

$5$ .

V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4}{20} - \frac{12854.20408163 \cdot 5}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.19

Combina los numeradores sobre el denominador común.

V = π (\frac{5508.94460641 \cdot 4 - 12854.20408163 \cdot 5}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{5508.94460641 \cdot 4 - 12854.20408163 \cdot 5}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.20

Multiplica

5508.94460641

$5508.94460641$ por

4

$4$ .

V = π (\frac{22035.77842565 - 12854.20408163 \cdot 5}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{22035.77842565 - 12854.20408163 \cdot 5}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.21

Multiplica

- 12854.20408163

$- 12854.20408163$ por

5

$5$ .

V = π (\frac{22035.77842565 - 64271.02040816}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{22035.77842565 - 64271.02040816}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.22

Resta

64271.02040816

$64271.02040816$ de

22035.77842565

$22035.77842565$ .

V = π (\frac{- 42235.2419825}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (\frac{- 42235.2419825}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.23

Mueve el negativo al frente de la fracción.

V = π (- \frac{42235.2419825}{20} + 432 ((\frac{{2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428}^{3}}{3}) - \frac{0^{3}}{3}))

$V = π (- \frac{42235.2419825}{20} + 432 ((\frac{{2.\overline{571428}}^{3}}{3}) - \frac{0^{3}}{3}))$

Paso 12.2.4.24

Eleva

2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 571428

$2.\overline{571428}$ a la potencia de

3

$3$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0^{3}}{3}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0^{3}}{3}))$

Paso 12.2.4.25

Elevar

0

$0$ a cualquier potencia positiva da como resultado

0

$0$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0}{3}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0}{3}))$

Paso 12.2.4.26

Cancela el factor común de

0

$0$ y

3

$3$ .

Toca para ver más pasos...

Paso 12.2.4.26.1

Factoriza

3

$3$ de

0

$0$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 (0)}{3}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 (0)}{3}))$

Paso 12.2.4.26.2

Cancela los factores comunes.

Toca para ver más pasos...

Paso 12.2.4.26.2.1

Factoriza

3

$3$ de

3

$3$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 \cdot 0}{3 \cdot 1}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 \cdot 0}{3 \cdot 1}))$

Paso 12.2.4.26.2.2

Cancela el factor común.

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 \cdot 0}{3 \cdot 1}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{3 \cdot 0}{3 \cdot 1}))$

Paso 12.2.4.26.2.3

Reescribe la expresión.

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0}{1}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - \frac{0}{1}))$

Paso 12.2.4.26.2.4

Divide

0

$0$ por

1

$1$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))$

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))$

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} - 0))$

Paso 12.2.4.27

Multiplica

- 1

$- 1$ por

0

$0$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} + 0))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3} + 0))$

Paso 12.2.4.28

Suma

\frac{17.00291545}{3}

$\frac{17.00291545}{3}$ y

0

$0$ .

V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3}))

$V = π (- \frac{42235.2419825}{20} + 432 (\frac{17.00291545}{3}))$

Paso 12.2.4.29

Combina

432

$432$ y

\frac{17.00291545}{3}

$\frac{17.00291545}{3}$ .

V = π (- \frac{42235.2419825}{20} + \frac{432 \cdot 17.00291545}{3})

$V = π (- \frac{42235.2419825}{20} + \frac{432 \cdot 17.00291545}{3})$

Paso 12.2.4.30

Multiplica

432

$432$ por

17.00291545

$17.00291545$ .

V = π (- \frac{42235.2419825}{20} + \frac{7345.25947521}{3})

$V = π (- \frac{42235.2419825}{20} + \frac{7345.25947521}{3})$

Paso 12.2.4.31

Para escribir

- \frac{42235.2419825}{20}

$- \frac{42235.2419825}{20}$ como una fracción con un denominador común, multiplica por

\frac{3}{3}

$\frac{3}{3}$ .

V = π (- \frac{42235.2419825}{20} \cdot \frac{3}{3} + \frac{7345.25947521}{3})

$V = π (- \frac{42235.2419825}{20} \cdot \frac{3}{3} + \frac{7345.25947521}{3})$

Paso 12.2.4.32

Para escribir

\frac{7345.25947521}{3}

$\frac{7345.25947521}{3}$ como una fracción con un denominador común, multiplica por

\frac{20}{20}

$\frac{20}{20}$ .

V = π (- \frac{42235.2419825}{20} \cdot \frac{3}{3} + \frac{7345.25947521}{3} \cdot \frac{20}{20})

$V = π (- \frac{42235.2419825}{20} \cdot \frac{3}{3} + \frac{7345.25947521}{3} \cdot \frac{20}{20})$

Paso 12.2.4.33

Escribe cada expresión con un denominador común de

60

$60$ , mediante la multiplicación de cada uno por un factor adecuado de

1

$1$ .

Toca para ver más pasos...

Paso 12.2.4.33.1

Multiplica

\frac{42235.2419825}{20}

$\frac{42235.2419825}{20}$ por

\frac{3}{3}

$\frac{3}{3}$ .

V = π (- \frac{42235.2419825 \cdot 3}{20 \cdot 3} + \frac{7345.25947521}{3} \cdot \frac{20}{20})

$V = π (- \frac{42235.2419825 \cdot 3}{20 \cdot 3} + \frac{7345.25947521}{3} \cdot \frac{20}{20})$

Paso 12.2.4.33.2

Multiplica

20

$20$ por

3

$3$ .

V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521}{3} \cdot \frac{20}{20})

$V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521}{3} \cdot \frac{20}{20})$

Paso 12.2.4.33.3

Multiplica

\frac{7345.25947521}{3}

$\frac{7345.25947521}{3}$ por

\frac{20}{20}

$\frac{20}{20}$ .

V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{3 \cdot 20})

$V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{3 \cdot 20})$

Paso 12.2.4.33.4

Multiplica

3

$3$ por

20

$20$ .

V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{60})

$V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{60})$

V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{60})

$V = π (- \frac{42235.2419825 \cdot 3}{60} + \frac{7345.25947521 \cdot 20}{60})$

Paso 12.2.4.34

Combina los numeradores sobre el denominador común.

V = π (\frac{- 42235.2419825 \cdot 3 + 7345.25947521 \cdot 20}{60})

$V = π (\frac{- 42235.2419825 \cdot 3 + 7345.25947521 \cdot 20}{60})$

Paso 12.2.4.35

Multiplica

- 42235.2419825

$- 42235.2419825$ por

3

$3$ .

V = π (\frac{- 126705.72594752 + 7345.25947521 \cdot 20}{60})

$V = π (\frac{- 126705.72594752 + 7345.25947521 \cdot 20}{60})$

Paso 12.2.4.36

Multiplica

7345.25947521

$7345.25947521$ por

20

$20$ .

V = π (\frac{- 126705.72594752 + 146905.18950437}{60})

$V = π (\frac{- 126705.72594752 + 146905.18950437}{60})$

Paso 12.2.4.37

Suma

- 126705.72594752

$- 126705.72594752$ y

146905.18950437

$146905.18950437$ .

V = π (\frac{20199.46355685}{60})

$V = π (\frac{20199.46355685}{60})$

Paso 12.2.4.38

Combina

π

$π$ y

\frac{20199.46355685}{60}

$\frac{20199.46355685}{60}$ .

V = \frac{π \cdot 20199.46355685}{60}

$V = \frac{π \cdot 20199.46355685}{60}$

Paso 12.2.4.39

Multiplica

π

$π$ por

20199.46355685

$20199.46355685$ .

V = \frac{63458.48631665}{60}

$V = \frac{63458.48631665}{60}$

V = \frac{63458.48631665}{60}

$V = \frac{63458.48631665}{60}$

V = \frac{63458.48631665}{60}

$V = \frac{63458.48631665}{60}$

V = \frac{63458.48631665}{60}

$V = \frac{63458.48631665}{60}$

Paso 13

Divide

63458.48631665

$63458.48631665$ por

60

$60$ .

V = 1057.64143861

$V = 1057.64143861$

Paso 14

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