## Thomas' Calculus 13th Edition

$8$
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 $L=-4(-1)-(-4)=4+4=8$