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Multivariable & Vectorhard
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Evaluate the line integral ∮CF⋅dr\oint_C \mathbf{F} \cdot d\mathbf{r}∮C​F⋅dr where F(x,y)=⟨−yx2+4y2,xx2+4y2⟩\mathbf{F}(x,y) = \langle \frac{-y}{x^2+4y^2}, \frac{x}{x^2+4y^2} \rangleF(x,y)=⟨x2+4y2−y​,x2+4y2x​⟩ and CCC is the ellipse x2+4y2=4x^2 + 4y^2 = 4x2+4y2=4 oriented counterclockwise.