I need help with the following demo:
Show that for a steerable surface $ \Sigma $ with $\partial \Sigma=C$ an oriented curve has to
$\int_{C} (f \nabla g+g \nabla f ) d \vec{r}=0$
for any functions f, g of class $ C^{2} $ with open domain containing $ \Sigma $
What I have tried was with conservative fields since the integrand is equal to $ \nabla (fg) $, but the conditions that are put in the conservative field theorem are different, so I think it is not right.