What is the integral from 0 to x of (e^{-t^2}) ?

The integral from 0 to x of (e^{-t^2}) is (sqrt(pi))/2 \erf(x)

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integral from 0 to x of (e^{-t^2})

\int_{0}^{x} (e^{- t^{2}}) d t

\frac{π}{2} erf (x)

Solution steps

\int_{0}^{x} e^{- t^{2}} d t

Use the nonelementary integral:

\int e^{- t^{2}} d t = \frac{π}{2} erf (t)

= [\frac{π}{2} erf (t)]_{0}^{x}

Compute the boundaries:

\frac{π}{2} erf (x)

= \frac{π}{2} erf (x)

What is the integral from 0 to x of (e^{-t^2}) ?
The integral from 0 to x of (e^{-t^2}) is (sqrt(pi))/2 \erf(x)