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Say you want to use the divergence theorem in conjunction with Stokes' theorem. So, from Stokes' you know: Line integral (F*T ds)= Surface integral (curl(F)*n)dS.

And you know that Surface integral(F*n)dS= Triple integral (div(F) dV))

But then, if you try to apply that to Stokes' you get: Triple integral (div(curl(F)) dV) which has to be 0, because div(curl(F))=0, right?

What's wrong with my reasoning?