1. ## Stoke's Theorem

I've used Stokes's theorem to show that for $\bold{F}(\bold{x})$ a vector field,

$\oint_C d\bold{x} \times \bold{F} = \int_S (d\bold{S} \times \nabla) \times \bold{F}$

where the curve C bounds the open surface S.

I'm then asked to "Verify this result when C is the unit square in the xy plane with opposite vertices at
(0,0,0) and (1,1,0) and $\bold{F}(\bold{x}) = \bold{x}$".

I do not know how to go about evaluating either of these integrals. Any advice would be appreciated.

Thanks

2. Actually, I can evaluate the LHS by writing it as $\oint_C \bold{x}'(t) \times \bold{x}(t) dt$. I don't know how to do the other, though.

3. Actually, I'm an idiot. I can do it. Thanks anyway