What is the integral from y/2 to 1/2 of e^{-x^2} ?

The integral from y/2 to 1/2 of e^{-x^2} is 0.46128…-0.88622…\erf(y/2)

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integral from y/2 to 1/2 of e^{-x^2}

\int_{\frac{y}{2}}^{\frac{1}{2}} e^{- x^{2}} d x

0.46128 \dots - 0.88622 \dots erf (\frac{y}{2})

Solution steps

\int_{\frac{y}{2}}^{\frac{1}{2}} 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)]_{\frac{y}{2}}^{\frac{1}{2}}

Compute the boundaries:

0.46128 \dots - 0.88622 \dots erf (\frac{y}{2})

= 0.46128 \dots - 0.88622 \dots erf (\frac{y}{2})

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What is the integral from y/2 to 1/2 of e^{-x^2} ?
The integral from y/2 to 1/2 of e^{-x^2} is 0.46128…-0.88622…\erf(y/2)