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

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

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

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

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

Solution steps

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

Compute the boundaries:

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

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

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