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Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

$ \displaystyle \int_C y^3 \, dx - x^3 \, dy $, $ C $ is the circle $ x^2 + y^2 = 4 $

$-24 \pi$

Vector Calculus

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Campbell University

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Idaho State University

Boston College

so even a disliking to grow the review of this with respect to X Ah, the ripped him off. This with respect to So here is three x square. So the derivative off this component with respect of exes. Syria minus three X square. Mine is the revealed This was respect. Who's ah to the wife Should be, Ah, three y square. Hey, so it should be minus three x square plus y square d A and the circle radio's for Ah, maybe it's even easier if we do a change of coordinate use. Ah, it was a portal crossing the so Oh, ex hos are Earl coz I see that why Khosrow size either and the a host road the road this's and this keeps us us This will gives us ah x square plus y square is throw square And, uh, Roe is from zero to radius is square with forged too And I said, Ah, it's a whole circle So oh, so that should be zero two to pie row Q d ro tc. So here inside the Gogol wrote with a fourth over four and we're probably too uh, Therefore, we are two to the four over for which is for and this is just a concert. So in the root, it's just beautification. Four times Supervise a pie and time stories twenty for pie.