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## Homework Statement

C is the directed curve forming the triangle (0, 0, 0) to (0, 1, 1) to (1, 1, 1) to (0, 0, 0).

Let F=(x,xy,xz) Find ∫F·ds.

## Homework Equations

## The Attempt at a Solution

My intial instinct was to check if it was conservative. Upon calculating:

∇xF=(0,-z,y)

I concluded that it isn't conservative. How do I apply Green's theorem for a three-dimensional vector field that is non-conservative?