Calculus (3rd Edition)

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

Chapter 16 - Multiple Integration - 16.4 Integration in Polar, Cylindrical, and Spherical Coordinates - Preliminary Questions - Page 879: 1



Work Step by Step

Since $x=r\cos \theta $ and $y=r\sin\theta $, where $r: 0\to 1$ and $\theta :0 \to 2\pi$, then $x^2+y^2=r^2\cos^2 \theta+r^2\sin^2 \theta=r^2$. Hence the right integral is $$\int_0^{2\pi}\int_0^1r^3drd\theta.$$ That is, (d) is the right answer.
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