By changing to polar coordinates, evaluate the integral (where a>0):
int[a,0]int[sqrt(a^2 - x^2), 0](x^2 + y^2)dydx
May aswell post here!
Draw a picture of the region of the limits.
The lower limits are x = 0 and y = 0, which tells you that both x > 0 and y > 0, which means you're dealing with the 1st quadrant of the cartesian axis system.
Sketching the upper y limit
gives:
Circle with centre (0,0), radius a.
So from that sketch you should see that, in polar, the limits range from .
And the radius ranges from . Which converts to: