What is the integral from 0 to 1 of integral from 0 to y of xye^{x^2} ?

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

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

\frac{e - 2}{4}

Decimal Notation

0.17957 \dots

Solution steps

\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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What is the integral from 0 to 1 of integral from 0 to y of xye^{x^2} ?
The integral from 0 to 1 of integral from 0 to y of xye^{x^2} is (e-2)/4