Calculus Examples

$f (x) = \frac{1}{\sin^{2} (x)}$

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.

$F (x) = \int \frac{1}{\sin^{2} (x)} d x$

Step 3

Convert from $\frac{1}{\sin^{2} (x)}$ to $\csc^{2} (x)$ .

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

Step 4

Since the derivative of $- \cot (x)$ is $\csc^{2} (x)$ , the integral of $\csc^{2} (x)$ is $- \cot (x)$ .

$- \cot (x) + C$

Step 5

The answer is the antiderivative of the function $f (x) = \frac{1}{\sin^{2} (x)}$ .

$F (x) =$ $- \cot (x) + C$