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

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

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

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

\frac{π erfi ( 2 ) - π erfi ( - 2 )}{2}

Solution steps

\int_{- 2}^{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)]_{- 2}^{2}

Compute the boundaries:

\frac{π erfi ( 2 ) - π erfi ( - 2 )}{2}

= \frac{π erfi ( 2 ) - π erfi ( - 2 )}{2}

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