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

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

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integral from 0 to z of e^{-x^2}

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

\frac{π}{2} erf (z)

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erf (x)]_{0}^{z}

Compute the boundaries:

\frac{π}{2} erf (z)

= \frac{π}{2} erf (z)

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\int_{3}^{5} x^{2} + 4 d x

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