Calculus Examples

$x^{3}$

Step 1

Write $x^{3}$ as a function.

$f (x) = x^{3}$

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.

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

Step 4

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

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

Step 5

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

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