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

解

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

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

解答ステップ

\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

非初等積分を使用する:

\int e^{x^{2}} d x = \frac{π}{2} erfi (x)

= - [\frac{π}{2} erfi (x)]_{1}^{e}

限度を計算する:

\frac{π erfi ( e ) - π erfi ( 1 )}{2}

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