Calculus Examples

$e^{- x^{2}}$

Step 1

Write $e^{- x^{2}}$ as a function.

$f (x) = e^{- x^{2}}$

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.

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

Step 4

$\int e^{- x^{2}} d x$ is a special integral. The integral is the error function.

$erf (x) + C$

Step 5

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

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