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## Homework Statement

##\mathscr{C}## is an ellipse ##\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1##

and ##\vec{F}(x,y) = <xy^2, yx^2>##

write ##\displaystyle \int_\mathscr{C} \vec{F} \cdot d\vec{s}## as a double integral using greens theorem and evaluate

## Homework Equations

##\displaystyle \int_\mathscr{C} (Pdx+Qdy) = \iint_\mathscr{C} \Bigg(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\Bigg)dA##

## The Attempt at a Solution

seems to be I need to use ##\nabla \times \vec{F} = \Bigg(0,0, \frac{\partial F_{2}}{\partial x} - \frac{\partial F_{1}}{\partial y}\Bigg) = (2xy-2yx)=0##

not sure about the double integral though, figured maybe this

##\displaystyle \int_{-a}^{a} \int_{-\sqrt{1-\frac{x^2}{a^2}-b^2}}^{\sqrt{1-\frac{x^2}{a^2}-b^2}}0dydx=0##

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