Calculus Examples

$- x^{2}$

Step 1

Write $- x^{2}$ as a function.

$f (x) = - x^{2}$

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.

$F (x) = \int - x^{2} d x$

Step 4

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$- \int x^{2} d x$

Step 5

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$- (\frac{1}{3} x^{3} + C)$

Step 6

Rewrite $- (\frac{1}{3} x^{3} + C)$ as $- \frac{1}{3} x^{3} + C$ .

$- \frac{1}{3} x^{3} + C$

Step 7

The answer is the antiderivative of the function $f (x) = - x^{2}$ .

$F (x) =$ $- \frac{1}{3} x^{3} + C$