Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 16 - Multiple Integration - 16.1 Integration in Two Variables - Exercises - Page 846: 28



Work Step by Step

\begin{align*} \int_{0}^{2} \int_{0}^{2}\left(x^{2}-y^{2}\right) d y d x&=\int_{0}^{2} \left(x^{2}y-\frac{1}{3}y^{3}\right) \bigg|_{0}^{2} d x\\ &=\int_{0}^{2} \left(2x^{2} -\frac{8}{3} \right) d x\\ &=\frac{2}{3}x^3-\frac{8}{3}x\bigg|_{0}^{2}\\ &=0 \end{align*}
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