Calculus 8th Edition

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

Chapter 15 - Multiple Integrals - 15.6 Triple Integrals - 15.6 Exercises - Page 1077: 9



Work Step by Step

Let us consider $I=\iiint_E y dV$ Here, $ I=\int_{0}^3 \int_{0}^{x} \int_{x-y}^{x+y} dz dy dx= \int_{0}^3 \int_{0}^{x} [yz]_{x-y}^{x+y} dy dx$ Further, $\int_{0}^1 \int_{0}^{1} [xy(e^{2-x^2-y^2})-xy(e^0)] dy dx=\int_{0}^{3} yx+y^2-yx+y^2 dy dx$ and $ \int_0^3[\dfrac{2}{3} (y^3)]_0^x=[2x^4]_0^3$ Hence, $\iiint_E y dV=\dfrac{27}{2}$
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