The question is attached.

For this question, this is what I plotted ( but I drew it uglier ): http://www.wolframalpha.com/input/?i=plot+x^2+-+2x+%2B+y^2+%3D+0+and+x^2+%2B+y^2+%3D+4

Here is the double integral I evaluated but is incorrect: http://www.wolframalpha.com/input/?i=integral+from+0+to+pi/2+(integral+from+2cos(theta)+to+2+(r^3+-+4r)+dr)+dtheta

Could someone tell me why it is incorrect? I suspect it's the integrand itself but I am not 100% sure. I tried 0 = f(x,y) = x^2 + y^2 - 4 = r^2 - 4 prior to multiplying it by the r in front of dr d(theta).

Any help would be greatly appreciated!

Thanks in advance!