What is the integral from 0 to 1/2 of e^{-x^2} ?

The integral from 0 to 1/2 of e^{-x^2} is 0.46128…

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integral from 0 to 1/2 of e^{-x^2}

\int_{0}^{\frac{1}{2}} e^{- x^{2}} d x

0.46128 \dots

Solution steps

\int_{0}^{\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)]_{0}^{\frac{1}{2}}

Compute the boundaries:

0.46128 \dots

= 0.46128 \dots

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What is the integral from 0 to 1/2 of e^{-x^2} ?
The integral from 0 to 1/2 of e^{-x^2} is 0.46128…