I'm specifically struggling on finding the integration bounds for $\theta$ as usually the bounds for the radius are clear to me. For example, for the problem
$\int\limits_{D} \log(x^2 + y^2) \, dA$ where D = $\{(x,y) \mid a^2 \leq x^2 + y^2 \leq b^2\}$, I got this far:
$\int_{b}^{a} \int_{\theta} r \log(r^2) \, \mathrm{d}\theta \, \mathrm{d}r $
However I cannot figure out what the limits of $\theta$ are, as I simply assumed anytime I saw the equation of a circle ($x^2+y^2$) we would be referring to the whole circle i.e from $0$ to $2\pi$, however that seems to be wrong.
Thank you!