Past exam of the mathematical methods II course of the University of Oxford / 2016 / 8 / c / Solution

By Stokes theorem, it suffices to calculate the boundary line integral. On the $xz$ plane, $y=0$ and $dy=0$, soThis exact differential has zero integral around a closed curve. ThereforeThe argument applies to any admissible spanning surface, including a curved one; the surface itself need not lie in the $xz$ plane.