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

解

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

\frac{e}{2} - \frac{π}{4} erfi (1)

解答ステップ

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

簡素化

x^{2} : xx

= \int_{0}^{1} xx e^{x^{2}} d x

部分積分を適用する

= [\frac{1}{2} e^{x^{2}} x - \int \frac{1}{2} e^{x^{2}} d x]_{0}^{1}

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= [\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)]_{0}^{1}

限度を計算する:

\frac{e}{2} - \frac{π}{4} erfi (1)

= \frac{e}{2} - \frac{π}{4} erfi (1)