Calculus (3rd Edition)

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

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Preliminary Questions - Page 623: 2



Work Step by Step

Since the area is given by $$ \text { Area }=\frac{1}{2} \int_{\alpha}^{\beta} f(\theta)^{2} d \theta $$ then the formula in polar coordinates is valid even if $f(\theta)$ takes on negative values because it gets squared.
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