Let be $f(r,\theta)$ a function defined over a circle of radius $R$ where $0\leq r\leq R$ and $\theta$ is defined as the angle being $0\leq \theta\leq 2\pi$. My question is how to calculate the double integral over the circle.
I guess that the answer is: $$\int_{0}^{2\pi}\int_{0}^Rf(r,\theta)r\;\mathrm{d}r\mathrm{d}\theta,$$ because if I change the function to cartesian coordinates, I write the integral in cartesian coordinates and finally I change the integral to polar coordinates is what I get.
Thanks!