Calculus 8th Edition

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: 3

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: $\int _0^yxe^{y^3}dx=\frac{1}{2}e^{y^3}y^2$ $\int _0^1\frac{1}{2}e^{y^3}y^2dy=\frac{1}{6}\left(e-1\right)$
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