Calculus Examples

$\frac{\sin (x)}{x}$

Step 1

Write $\frac{\sin (x)}{x}$ as a function.

$f (x) = \frac{\sin (x)}{x}$

Step 2

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 3

Set up the integral to solve.

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

Step 4

$\int \frac{\sin (x)}{x} d x$ is a special integral. The integral is the sine integral function.

$S i (x) + C$

Step 5

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

$F (x) =$ $S i (x) + C$