Evaluate ∬(x^2+y^2)^2/(x^2y^2) dx dy over the region common to the circles x^2+y^2=7x and x^2+y^2=11y.
The circles are
(x-7/2)^2 + y^2 = 49/4
x^2 + (y-11/2)^2 = 121/4
They intersect at (0,0) and (847/170,539/170)
So, just evaluate the integral
∫[0,847/170]∫[11/2-√(121/4-x^2),√(49/4-(x-7/2)^2)] (x^2+y^2)^2/(x^2y^2) dy dx
∫[0,847/170] y^3/3x^2 - x^2/y + 2y [11/2-√(121/4-x^2),√(49/4-(x-7/2)^2)]
∫[0,847/170] (49+28x-8x^2)/(3√(7x-x^2)) + (8√(121-4x^2)+121(√(121-4x^2)-11))/(6x^2) dx
Hmmm. Those x's in the bottom pose a problem when x=0. Better check my math.