Applying Divergence Theorem to Stokes' Theorem

[schaefera]

Not really a homework problem, just me wondering about this: why is there a problem here?

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?

 

[ckutlu]

I think you should check if one of the theorem states the surface as a "closed" one.