Calculus Examples

$\sec^{2} (θ)$

Write $\sec^{2} (θ)$ as a function.

$f (θ) = \sec^{2} (θ)$

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

$F (θ) = \int f (θ) d θ$

Set up the integral to solve.

$F (θ) = \int \sec^{2} (θ) d θ$

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

$\tan (θ) + C$

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

$F (θ) =$ $\tan (θ) + C$