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## Homework Statement

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

## Homework Equations

Divergence theorem:

∫∫∫∇.FdV = ∫∫∇.ndS

Stokes theorem:

∫∫(∇xF).n dS = ∫F.dR

## The Attempt at a Solution

The divergence theorem gives a dot product. Here we're asked for the cross product

∫∫(∇xF).n dS

but the divergence of the curl will be 0. The Stokes theorem applied here is nonzero. What's wrong?