- #1

MacLaddy

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## Homework Statement

Use Green's Theorem to evaluate [itex]\int_c(x^2ydx+xy^2dy)[/itex], where c is the positively oriented circle, [itex]x^2+y^2=9[/itex]

## Homework Equations

[tex]\int\int_R (\frac{\delta g}{\delta x}-\frac{\delta f}{\delta y})dA[/tex]

## The Attempt at a Solution

I have found [itex]\frac{\delta g}{\delta x}-\frac{\delta f}{\delta y}[/itex] to be [itex]y^2-x^2[/itex]

My hangup is moving forward. My integral will look like this,

[itex]\int\int_R [y^2-x^2]dA[/itex]

however, since the region is a circle I am integrating over should I convert this to polar? If I do, will my values in the integral be [itex]rcos^2\theta - rsin^2\theta[/itex], or since it's basically just a line integral, will it be [itex]3cos^2\theta - 3sin^2\theta[/itex]?

This setup is confusing me. Any help is appreciated. Am I integrating just the perimeter of the circle, or the entire thing?

Thanks,

Mac

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