Mathematics

Both curves are circles in disguise—converting to Cartesian form reveals they're circles of radius 2 centered at $(0,2)$ and $(2,0)$ respectively. The key is recognizing that their intersection points occur where $\sin\theta = \cos\theta$, and the overlapping region is symmetric. You'll need to set up a polar integral that captures only the shared area, being careful about which curve bounds the region in each angular interval.

Both curves are circles in disguise—converting to Cartesian form reveals they're circles of radius 2 centered at $(0,2)$ and $(2,0)$ respectively. The key is recognizing that their intersection points occur where $\sin\theta = \cos\theta$, and the overlapping region is symmetric. You'll need to set up a polar integral that captures only the shared area, being careful about which curve bounds the region in each angular interval.