By Green's theorem, ∮C(y2 dx+x2 dy)\displaystyle\oint_C (y^2\,dx + x^2\,dy)∮C(y2dx+x2dy) equals ∬D\displaystyle\iint_D∬D:
∬D(2x−2y) dA\displaystyle\iint_D (2x - 2y)\,dA∬D(2x−2y)dA
∬D(x2−y2) dA\displaystyle\iint_D (x^2 - y^2)\,dA∬D(x2−y2)dA
∬D0 dA\displaystyle\iint_D 0\,dA∬D0dA
∬D2xy dA\displaystyle\iint_D 2xy\,dA∬D2xydA