MATH 210 Study Guide - Final Guide: Simply Connected Space, Automobilclub Von Deutschland, Surface Integral
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Problem 1 solution: (a) compute the integral ic. F d s where c is the circle x2 + y2 = 1 of radius 1 centered at the origin, traversed counterclockwise, starting and ending at the point (1, 0) for. F = hp, qi = (cid:28) y x2 + y2 , x x2 + y2(cid:29) (b) for the vector eld in part (a), we know that. Solution: (a) we evaluate the vector line integral using the formula: A parameterization of c is r (t) = hcos(t), sin(t)i, 0 t 2 . The derivative is r (t) = h sin(t), cos(t)i. Using the fact that x = cos(t) and y = sin(t) from the parameterization, the vector eld f written in terms of t is: y x2 + y2 , F = h sin(t), cos(t)i sin(t) cos2(t) + sin2(t) x x2 + y2(cid:29) cos(t) cos2(t) + sin2(t)(cid:29) Thus, the value of the line integral is:
