Question

model & compute the length L of the cardioid whose polar model is r(0)=2-2cos(0), 0<0<2pie

Answer 1

\[dr/d \theta = 2\sin \Theta = L = \int\limits_{0}^{2\Pi}\sqrt{r^2*dr/d \theta}\]

Answer 2

\[L=\int\limits_{0}^{2\Pi}(2-2\cos \theta)^2*2\sin \theta\]

Answer 3

\[L=\int\limits_{0}^{2\Pi}\sqrt{(2-2\cos \theta)^2*2\sin \theta)}\]