(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the line integral

I = (x2z + yzexy) dx + xzexy dy + exy dz

where C is the arc of the ellipse r(t) = (cost,sint,2−sint) for 0 <= t <= PI.

[Hint: Do not compute this integral directly. Find a suitable surface S such that C is a part of the boundary ∂S and use Stokes’ theorem.]

2. Relevant equations

Stoke's theorem

3. The attempt at a solution

Because this is from 0 to Pi, this is an open curve? Can you compute the integral using stokes theorem over the surface from 0 to 2Pi, so you have a closed curve and then divide that answer by two to get the open curve 0 to Pi?

I'm confused on what techniques to use when the curve is open.

any help would be wonderful. Thanks in advance!

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# Homework Help: Stoke's Theorem

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