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## Homework Statement

Use Stokes' Theorem to evaluate ∫

_{c}F ⋅ dr, where F(x, y, z) = x

^{2}z

**i**+ xy

^{2}

**j**+ z

^{2}

**k**and C is the curve of the intersection of the plane x + y + z = 1 and the cylinder x

^{2}+ y

^{2}= 9 oriented counterclockwise as viewed from above.

## Homework Equations

Stoke's Theorem:

∫

_{c}F ⋅ dr = ∫

_{s}curlF ⋅ ds

## The Attempt at a Solution

For this problem I am extremely confused of which variant of Stoke's theorem to use and when it is appropriate to use a certain variant. For this problem my teacher found the curlF and then dotted it with the ds. However there are problems in the same section where he uses the left side of Stoke's Theorem. Is it possible to use both? If so, would it be possible to say which would be more advantageous over the other?