Evaluating ∫∫(∇xF).n dS: Divergence vs. Stokes' Theorem

[jaejoon89]

Given F = xyz i + (y^2 + 1) j + z^3 k
Let S be the surface of the unit cube 0 ≤ x, y, z ≤ 1. Evaluate the surface integral ∫∫(∇xF).n dS using
a) the divergence theorem
b) using Stokes' theorem


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Since the divergence theorem involves a dot product rather than a curl,how would it apply in this problem (which asks for the curl)?

 

[nickjer]

You would treat \nabla \times F as a new vector, and just use it in the divergence theorem.

 

[dx]

Hi jaejoon89,

You already posted this question, and someone has replied to it. If you have any further questions, use the same thread.