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 (sqrt(pi))/2 \erfi(1/2)

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

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

\frac{π}{2} erfi (\frac{1}{2})

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} erfi (x)

= [\frac{π}{2} erfi (x)]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{π}{2} erfi (\frac{1}{2})

= \frac{π}{2} erfi (\frac{1}{2})

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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 (sqrt(pi))/2 \erfi(1/2)