Find the double integral of : -

Question

Find the double Integral of ((x-y)^2)/(x^2+y^2)

Answer 1

need region in xy plane to evaluate any double integral f(x,y)dxdy.

reason, say dx part evaluated first and ∫f(x,y)dx=F(x,y)+C(y)

C can be a constant or any function of y.

example C=sin(y)+e^y*cos(y)+y⁴+8

that makes evaluating the integral [F(x,y)+C(y)dy part impossible