Answer
$\frac{1}{6} (e-1)$
Work Step by Step
$\int _0^1\int _0^yxe^{y^3}dxdy$
Take derivative with respect to x and then y:
$\int _0^yxe^{y^3}dx=\frac{1}{2}e^{y^3}y^2$
$\int _0^1\frac{1}{2}e^{y^3}y^2dy=\frac{1}{6}\left(e-1\right)$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 15 - Multiple Integrals - 15.2 Double Integrals over General Regions - 15.2 Exercises - Page 1048: 3
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