# Divergence theorem

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)?

## Answers and Replies

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

dx
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Hi jaejoon89,

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