I have this question in my review problems for multivariable calculus. The hint is to change the coordinates to polar coordinates, however, I am not sure how to change the limits of the integrals. Any help with this will be greatly appreciated!
$$\int_{0}^{2a} \int_{-\sqrt{2ay-y^2}}^{0} \sqrt{x^2+y^2} dxdy$$
In this problem, a is a positive number.
Work out exactly what the region is, then describe that region in terms of polar instead of rectangular coordinates. The first task is to figure out what the graph of $x=-\sqrt{2ay-y^2}$ look like.
HINT: If $x=-\sqrt{2ay-y^2}$, then $x^2=2ay-y^2$, and $x^2+(y-a)^2=a^2$.