Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 15 - Multiple Integrals - Review - Exercises - Page 1102: 21

Answer

$\frac {e^{6}-7}{2}$

Work Step by Step

Since, $R=(r,\theta) | 2\leq r\leq 4, 0\leq \theta \leq \pi$ $\int\int_{R} ye^{xy}dA=\int_{0}^{3}\int_{0} ^{2}ye^{xy}dxdy$ $=\int_{0}^{3}[e^{xy}]_{0} ^{2}dy$ $=\int_{0}^{3}[e^{2y}-1]dy$ $=\frac {1}{2}[e^{2y}-y]_{0} ^{3}$ $=[\frac {e^{6}}{2}-3]-\frac{1}{2}$ $=\frac {e^{6}-7}{2}$
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