Calculus Examples

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

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.

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

Step 3

Since $- 2$ is constant with respect to $x$ , move $- 2$ out of the integral.

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

Step 4

Since the derivative of $\tan (x)$ is $\sec^{2} (x)$ , the integral of $\sec^{2} (x)$ is $\tan (x)$ .

$- 2 (\tan (x) + C)$

Step 5

Simplify.

$- 2 \tan (x) + C$

Step 6

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

$F (x) =$ $- 2 \tan (x) + C$