Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 15 - Section 15.6 - Triple Integrals - 15.6 Exercise - Page 1037: 9



Work Step by Step

Consider $I=\iiint_E y dV$ $ 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$ or, $=\int_{0}^1 \int_{0}^{1} [xye^{2-x^2-y^2}-xye^0] dy dx$ or, $= \int_{0}^{3} [yx+y^2-yx+y^2] dy dx$ or, $= \int_0^3(2/3) y^3|_0^x$ or, $=[\dfrac{2x^4}{1}|_0^3$ or, $=\dfrac{27}{2}$
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