Calculus 8th Edition

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

Chapter 15 - Multiple Integrals - Review - Exercises - Page 1102: 8



Work Step by Step

$\int_{0}^{1}\int_{0}^{y}\int_{x}^{1}6xyzdzdxdy=\int_{0}^{1}\int_{0}^{y}xy[3z^{2}]|_{x}^{1}dxdy$ $=\int_{0}^{1}\int_{0}^{y}xy[3-3x^{2}]dxdy$ $=\int_{0}^{1}\int_{0}^{y}[3xy-3x^{3}y]dxdy$ $=\frac{3y^{4}}{8}-\frac{3y^{6}}{24}|_{0}^{1}$ $=\frac{3}{8}-\frac{1}{8}$ $=\frac{1}{4}$
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