Q: Obtain the area inside $\displaystyle r=1+cos\theta$ and outside $\displaystyle r=3cos\theta$

My first attempt was $\displaystyle A=2\int_{\frac{\pi}{3}}^{\pi}\int_{3cos\theta}^{1+ cos\theta}rdrd\theta$ which I quickly realized has incorrect angles, since $\displaystyle r=3cos\theta$ loops around twice as fast as the other graph. Thank you!

EDIT - I have just figured it out on my own! Sorry about that