I'm just trying to figure out something regarding Cap-Independence. The problem reads
$\partial S:= r(t)=(\cos t,\sin t,\sin 2t)$, $0\le t \le 2\pi;$
$\phi=z\,dzdx-6y^2dxdy$ ($\partial S $ represents the boundary of S).
The problem states: Show $\int \phi$ over S cap-independent and use this fact to compute it.
Now it is is easy to find a $\phi = d\psi$ which implies that the form is exact and thus is cap-independent. However I am at a loss for how to apply any theorems or translations to use the fact that phi is cap-independent in the computation of this problem. (This is the first time I've encountered cap-independence).