What is the integral from a to b of e^{-x^2} ?

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

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integral from a to b of e^{-x^2}

\int_{a}^{b} e^{- x^{2}} d x

\frac{π}{2} erf (b) - \frac{π}{2} erf (a)

Solution steps

\int_{a}^{b} 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)]_{a}^{b}

Compute the boundaries:

\frac{π}{2} erf (b) - \frac{π}{2} erf (a)

= \frac{π}{2} erf (b) - \frac{π}{2} erf (a)

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