Calculus Examples

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

Step 1

The function $f (x)$ can be found by evaluating the indefinite integral of the derivative $f' (x)$ .

$f (x) = \int f' (x) d x$

Step 2

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

$S (x) + C$

Step 3

The function $f$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

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