Calculus Examples

$f (x) = x^{6}$

Step 1

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 2

Set up the integral to solve.

$F (x) = \int x^{6} d x$

Step 3

By the Power Rule, the integral of $x^{6}$ with respect to $x$ is $\frac{1}{7} x^{7}$ .

$\frac{1}{7} x^{7} + C$

Step 4

The answer is the antiderivative of the function $f (x) = x^{6}$ .

$F (x) =$ $\frac{1}{7} x^{7} + C$