## Calculus 8th Edition

$\frac{1}{6} (e-1)$
$\int _0^1\int _0^yxe^{y^3}dxdy$ Take derivative with respect to x and then y: $\int _0^yxe^{y^3}dx=\frac{1}{2}e^{y^3}y^2$ $\int _0^1\frac{1}{2}e^{y^3}y^2dy=\frac{1}{6}\left(e-1\right)$