Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 11: Parametric Equations and Polar Coordinates - Practice Exercises - Page 689: 51



Work Step by Step

As we are given that $r=-1+\cos \theta$ Length of the curve is: $L= \int_{0}^{2\pi} \sqrt{(-1+\cos \theta)^2+(-\sin \theta)^2} d\theta$ This gives: $L=2 \int_{0}^{2\pi} \sin (\dfrac{\theta}{2}) d\theta$ This implies that $L=-4(-1)-(-4)=4+4=8$
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