- #1

Saladsamurai

- 3,019

- 6

## Homework Statement

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] and

*C*is the curve of the intersection of the plane [itex]x+y+z=1[/itex] and the cylinder

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

(

*C*is oriented clockwise when viewed from above.)

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

## Homework Equations

Stoke's Theorem## 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*. Now

*S*is the surface that is bounded by

*C*right? If not, please stop me here.