Evaluate $\iint_Rxy^2\sqrt{x^2+y^2}dxdy$, where $R={(xy)\in{\Bbb{R}^2}:1\le{x^2}+y^2\le{4},y\ge{0}}.$ I have no idea where to start with this one? And how to step through it.
How would I set the limits for this? And then what would I go on to do?
Thanks!

if you switch to polar coordinates the integral becomes:
$$
\int_{r=1}^{r=2} \int_0^{\pi} r^5 \cos \theta \sin^2 \theta d\theta dr
$$
