University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 273: 99


$r=\cos \pi \theta -1$

Work Step by Step

We need to find the anti-derivative for $\dfrac{dr}{d \theta}=-\pi \sin \pi \theta $ Thus, we have $r=\cos \pi \theta +C$ Apply the initial condition $r(0)=0$ in the above equation to solve for $C$. we get $1+C=0 \implies C=-1$ Hence, $r=\cos \pi \theta -1$
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