I agree with your set up and calculation.I want to find the area inside and outside (we're in polar coordinates).
After making a sketch and finding the intersection points at , I set up the integral
thinking it would give me the area I want, and obtained .
However, the answer in the back of my textbook is .
I checked the actual integration in Maple, so either the integral was set up incorrectly or the back of the textbook answer is wrong. I can't see what if anything I've done wrong, however I'm quite rusty at these types of problems so I wanted to ask if you see anything wrong with what I did. Thanks in advance.