Calculus Examples

$\sin (x^{2})$

Step 1

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

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

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.

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

Step 4

$\int \sin (x^{2}) d x$ is a special integral. The integral is the Fresnel integral function.

$S (x) + C$

Step 5

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

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