Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Section 15.1 - Double and Iterated Integrals over Rectangles - Exercises 15.1 - Page 875: 26



Work Step by Step

V=$\int\int f(x,y)dA$ =$\int^{2}_{0} \int^{2}_{0}(16-x^2-y^2)dy dx$ =$\int^{2}_{0}[16-x^2y-\frac{1}{3}y^3]^2_0dx$ =$\int^{2}_{0}(\frac{88}{3}-2x^2)dx$ =$[\frac{88}{3}x-\frac{2}{3}x^3]^2_0$ =$\frac{160}{3}$
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