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Math Help - Stoke's Theorem

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    Actually, I'm an idiot. I can do it. Thanks anyway
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