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11 Nov 2019
Compute each of the following in two ways: as given and by using Green's Theorem to rewrite it. where C is the circle x2 + y2 = 36 (oriented positively) and (x,y) = -y,x . (Hint or warning: you'll need to give a parametrization of the circle to do this directly, but once it's rewritten using Green's Theorem the double integral should be easy.) where R is the disk of radius 2 centered at the origin. (Hint or warning: here the direct way do the double integral - is fairly easy, and a review of stuff from Exam 2. Using Green's theorem involves picking P, Q so that . Any P and Q with that property will do. and again, chosing a parametrization of the curve, in this case the circle bounding the disk with positive orientation.)
Compute each of the following in two ways: as given and by using Green's Theorem to rewrite it. where C is the circle x2 + y2 = 36 (oriented positively) and (x,y) = -y,x . (Hint or warning: you'll need to give a parametrization of the circle to do this directly, but once it's rewritten using Green's Theorem the double integral should be easy.) where R is the disk of radius 2 centered at the origin. (Hint or warning: here the direct way do the double integral - is fairly easy, and a review of stuff from Exam 2. Using Green's theorem involves picking P, Q so that . Any P and Q with that property will do. and again, chosing a parametrization of the curve, in this case the circle bounding the disk with positive orientation.)