area of the region that lies inside both curves

Hi,

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.