# Polar Coordinates Double Integral Question

Evaluate $\int(x^2+y^2)^{1/2}dA$ where $D$ is region enclosed by the two circles: $x^2+y^2=64$ and $x^2+(y-4)^2=16$.

I'm confused on what the limits of integration for the corresponding double integral will be once converted to polar coordinates?

You're integrating the region between two circles, one with centre at the origin and radius 8, one with centre at $(0,4)$ and radius 4. To solve the problem, find the angles of the points where the circles intersect to get the limits of integration for $\theta$ and use the equations of the circles as your upper and lower limits of integration for the radius.
• Hint: when the points intersect, $x^2 + y^2 = 64 = 8y$ – Bob Roberts Apr 5 '16 at 0:30