Verify Green's theorem for $$ M = -y/(y^2 + x^2) $$ $$ N = x/(y^2 + x^2) $$
$$ R = \{ (x,y) / h^2 \le x^2 + y^2 \le 1 \} $$ where $ 0 \lt h \le 1 $
My attempt:
$ \int Mdx + Ndy = \int_0^{2\pi} \alpha d\alpha = 2\pi $
But while calculating RHS of stokes i.e. $ \iint\frac{dN}{dx} -\frac{dM}{dy} dxdy = 0 $ as integrand vanishes.
How to approach this RHS.