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

Use Stoke's Theorem to calculate [itex]\int_C\vec{F}\cdot\, dr[/itex], where

[itex]\vec{F}=<x^2z\, ,xy^2\,,z^2>[/itex] andCis the curve of the intersection of the plane [itex]x+y+z=1[/itex] and the cylinder

[itex]x^2+^2=9[/itex].

(Cis oriented clockwise when viewed from above.)

Answer: [itex]\frac{81}{2}\pi[/itex].

2. Relevant equationsStoke's Theorem

3. The attempt at a solution

Okay, let me try to explain where I am getting lost. Firstly, I know that the premise of Stoke's Theorem is that is relates a line integral to a Surface integral.

When I graph this, I get a cylinder that is symmetrical about the z-axis and it is intersected by a plane which results in an ellipse. (see terrible drawing below)

Now, I need to parametrize (how do you spell that anyway?)S. NowSis the surface that is bounded byCright? If not, please stop me here.

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# Stoke's Theorem

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