Calculus Examples

$11 \cdot 4 x^{3}$

Step 1

Write $11 \cdot 4 x^{3}$ as a function.

$f (x) = 11 \cdot 4 x^{3}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int 11 \cdot (4 x^{3}) d x$

Step 4

Multiply $4$ by $11$ .

$\int 44 x^{3} d x$

Step 5

Since $44$ is constant with respect to $x$ , move $44$ out of the integral.

$44 \int x^{3} d x$

Step 6

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$44 (\frac{1}{4} x^{4} + C)$

Step 7

Simplify the answer.

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Step 7.1

Rewrite $44 (\frac{1}{4} x^{4} + C)$ as $44 (\frac{1}{4}) x^{4} + C$ .

$44 (\frac{1}{4}) x^{4} + C$

Step 7.2

Simplify.

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Step 7.2.1

Combine $44$ and $\frac{1}{4}$ .

$\frac{44}{4} x^{4} + C$

Step 7.2.2

Cancel the common factor of $44$ and $4$ .

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Step 7.2.2.1

Factor $4$ out of $44$ .

$\frac{4 \cdot 11}{4} x^{4} + C$

Step 7.2.2.2

Cancel the common factors.

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Step 7.2.2.2.1

Factor $4$ out of $4$ .

$\frac{4 \cdot 11}{4 (1)} x^{4} + C$

Step 7.2.2.2.2

Cancel the common factor.

$\frac{4 \cdot 11}{4 \cdot 1} x^{4} + C$

Step 7.2.2.2.3

Rewrite the expression.

$\frac{11}{1} x^{4} + C$

Step 7.2.2.2.4

Divide $11$ by $1$ .

$11 x^{4} + C$

Step 8

The answer is the antiderivative of the function $f (x) = 11 \cdot (4 x^{3})$ .

$F (x) =$ $11 x^{4} + C$