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

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

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

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

\frac{π}{2} erf (x)

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erf (y)]_{0}^{x}

Compute the boundaries:

\frac{π}{2} erf (x)

= \frac{π}{2} erf (x)

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