Double integral over annulus 
Evaluate $$\iint_D\ e^{-x^2 - y^2}\ dA,$$
  where $D$ is annulus $a \le x^2 + y^2 \le b$

My understanding is it involves polar coordinates but I don't understand how to convert it.

Since $r^2 = x^2 + y^2$ (do you see why?), we're considering the annulus $\sqrt{a} \le r \le \sqrt{b}$. Then the integral is
$$\iint_D\ e^{-r^2}\ dA,$$
The area element is $dA = r\ dr\ d\theta$ in polar coordinates. Now what do you make the limits of integration?
