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

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

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integral from-x to x of e^{-u^2}

\int_{- x}^{x} e^{- u^{2}} d u

\frac{π}{2} erf (x) - \frac{π}{2} erf (- x)

Solution steps

\int_{- x}^{x} e^{- u^{2}} d u

Use the nonelementary integral:

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

= [\frac{π}{2} erf (u)]_{- x}^{x}

Compute the boundaries:

\frac{π}{2} erf (x) - \frac{π}{2} erf (- x)

= \frac{π}{2} erf (x) - \frac{π}{2} erf (- x)

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