Calculus 8th Edition

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

Chapter 15 - Multiple Integrals - Review - True-False Quiz - Page 1101: 2


False, the two integrals describe different areas of integration.

Work Step by Step

Note that $\int_{0}^{1} \int_{0}^{x} \sqrt(x+y^2) \, dy \, dx \neq \int_{0}^{x} \int_{0}^{1} \sqrt(x+y^2) \, dx \, dy$ because the area of integration is different. We must switch the integration bounds to $\int_{0}^{1} \int_{y}^{1} \sqrt(x+y^2) \, dx \, dy$ to ensure the same area of integration and thus equality.
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