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: 25



Work Step by Step

V=$\int\int f(x,y)dA$ =$\int^{1}_{-1} \int^{1}_{-1}(x^2+y^2)dy dx$ =$\int^{1}_{-1}[x^2y+\frac{1}{3}y^3]^1_{-1}dx$ =$\int^{1}_{-1}(2x^2+\frac{2}{3})dx$ =$[\frac{2}{3}x^3+\frac{2}{3}x]^1_{-1}$ =$\frac{8}{3}$
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