area of the region that lies inside both curves
I am trying to solve this problem:
Find the area of the region that lies inside both curves.
Which are the circles and on the Cartesian coordinate system.
When I try to solve the problem in the following way, I get a different answer than in my textbook:
However, if I do it by symmetry, it gives me a different answer (the correct answer in my textbook):
Can anyone explain this to me? I've been trying to figure it out, but I can't seem to get it.