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人気のある微分積分 >

integral from 0 to 1 of integral from 0 to y of xye^{x^2}

解

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

解

\frac{e - 2}{4}

+1

十進法表記

0.17957 \dots

解答ステップ

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

\int_{0}^{y} x y e^{x^{2}} d x = \frac{y ( e ^{y^{2}} - 1 )}{2}

= \int_{0}^{1} \frac{y ( e ^{y^{2}} - 1 )}{2} d y

\int_{0}^{1} \frac{y ( e ^{y^{2}} - 1 )}{2} d y = \frac{e - 2}{4}

= \frac{e - 2}{4}

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