Calculus Examples

$f (x) = \sin (x)$

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.

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

Step 3

The integral of

$\sin (x)$ with respect to

$x$ is

$- \cos (x)$ .

$- \cos (x) + C$

Step 4

The answer is the antiderivative of the function

$f (x) = \sin (x)$ .

$F (x) =$

$- \cos (x) + C$