Write an integral expression for the area for ...
\item the intersection of the regions enclosed by r = sin θ and r = cos θ
This is the region whose area we're looking for:
If we look closely, we see that this region consists of 2 parts. One part is bounded just by the graph of cos θ, and the other part is bounded just by the graph of sin θ.
The part that's bounded by sin θ goes from θ = 0 to , and the part that's bounded by cos θ goes from to .
The area of the part bounded by sin θ is
and the area of the part bounded by cos θ is
Adding these, we find that the area of the region is