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## Homework Statement

Let

[tex]\vec{F}=xyz\vec{i}+(y^{2}+1)\vec{j}+z^{3}\vec{k}[/tex]

And let S be the surface of the unit cube in the first octant. Evaluate the surface integral:

[tex]

\int\int_{S} \nabla\times \vec{F} \cdot \vec{n} dS

[/tex]

using:

a) The divergence theorem

b) Stoke's theorem

c) Direct computation

## Homework Equations

Divergence Theorem:

[tex]\int\int\int\nabla \bullet \vec{F} dV = \int\int \vec{F} \bullet \vec{n} dS[/tex]

## The Attempt at a Solution

I think I have b and c worked out but part a I am not sure of. What I don't understand is how I can use the divergence theorem here. If I substitute [tex] F = curl(F)[/tex] into the divergence theorem I will get zero by identity. So, how is that possible to evaluate? If someone could pelase tell me what I'm doing wrong I would greatly appreciate it.

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