Calculus Examples

$(\sec^{2} (x))$

Write $(\sec^{2} (x))$ as a function.

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

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

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

Set up the integral to solve.

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

Remove parentheses.

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

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

$\tan (x) + C$

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

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