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

The integral from e to 1 of e^{x^2} is -(sqrt(pi)\erfi(e)-sqrt(pi)\erfi(1))/2

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

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

- \frac{π erfi ( e ) - π erfi ( 1 )}{2}

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{e} 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)]_{1}^{e}

Compute the boundaries:

\frac{π erfi ( e ) - π erfi ( 1 )}{2}

= - \frac{π erfi ( e ) - π erfi ( 1 )}{2}

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

\int_{0}^{2} 7 x + 1 d x

\int_{1}^{5} \frac{3}{3 x - 2} d x

\int_{- 1}^{1} 2 x^{2} - x + 6 d x

\int_{0}^{x} (e^{x^{2}}) d x

What is the integral from e to 1 of e^{x^2} ?
The integral from e to 1 of e^{x^2} is -(sqrt(pi)\erfi(e)-sqrt(pi)\erfi(1))/2