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13 Nov 2019
5. Consider the following integral, which does not seem very easy to evaluate. 2Ï eloo co s2(t) sin(1 + e30cow(t) )sin(t) + cos2(t) dt In this problem we will evaluate the integral by using Green's theorem. Let c be the circle of radius 1 centered at (0,0), and oriented counterclockwise. One possible param- eterization of c is c(t) (cos(t), sin(t)) with t ⬠[0, 2 (a) Find a vector field F so that when evaluating , F ds using the parameterization above, the integral that results is () (b) Use Green's theorem to convert this to an integral over the unit disc, and evaluate that integral.
5. Consider the following integral, which does not seem very easy to evaluate. 2Ï eloo co s2(t) sin(1 + e30cow(t) )sin(t) + cos2(t) dt In this problem we will evaluate the integral by using Green's theorem. Let c be the circle of radius 1 centered at (0,0), and oriented counterclockwise. One possible param- eterization of c is c(t) (cos(t), sin(t)) with t ⬠[0, 2 (a) Find a vector field F so that when evaluating , F ds using the parameterization above, the integral that results is () (b) Use Green's theorem to convert this to an integral over the unit disc, and evaluate that integral.
Casey DurganLv2
22 Sep 2019