# Divergence theorem

1. May 4, 2009

### 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

---

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

2. May 4, 2009

### nickjer

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

3. May 4, 2009

### dx

Hi jaejoon89,

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