Use a double integral to find the area of the region. The region inside the circle $(x − 2)^2 + y^2 = 4$ and outside the circle $x^2 + y^2 = 4$.
I understand how to get the limits of integrand for this region on $r$ and $\theta$, but when you set up the integral it is as follows.
The general form of a double integral in polar is:
$$\iint f(r\cos(\theta), r\sin(\theta)) r \, dr \, d\theta$$
However when evaluating this integral it becomes:
$$\iint r \, dr \, d\theta$$
Can someone please explain why
$$f(r\cos(\theta), r\sin(\theta)) =1$$