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: 5



Work Step by Step

Note that $\int_{0}^{1} f(x) \, dx = \int_{0}^{1} f(y) \, dy$ as the area of integration of $f$ stays the same with both equations. Thus, $\int_{0}^{1} \int_{0}^{1} f(x) f(y) \, dy \, dx = \int_{0}^{1} f(x) \, dx \int_{0}^{1} f(y) \, dy = \left[ \int_{0}^{1} f(x) \, dx \right]^2$.
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