Answer
$\frac{1}{6}\left(e-1\right)$
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: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 15 - Section 15.2 - Double Integrals over General Regions - 15.2 Exercise - Page 1008: 3
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