Question

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Find the circulation of the vector field F(x, y) = P(x, y)i + Q(x, y)j where P(x, y) = [2 − y] / [9x^2 + (y − 2)^2] + [−2 − y / [9x^2 + (y + 2)^2] , Q(x, y) = x / [9x^2 + (y − 2)^2] + x / [9x ^2 + (y + 2)^2] , around the simple closed curve C = C1 ∪ C2, where C1 is the path along the line y = x from (−3, −3) to (3, 3), and C2 is the path counterclockwise along the circle x 2+y 2 = 18 from (3, 3) to (−3, −3).

Find the circulation of the vector field P(ar, y)i +Q(x, y)j F(ar,y) where 2-y P(x, y) = 9x2 + (y - 2)2 -2 y 9r2 + (y+ 2)?'| Q(x, y) = 9r2 + (y- 2)? * 9xr2 + (y + 2)2' around the simple closed curve C = Ci U C2, where C1 is the path along the line y = x from (-3, -3) to (3,3), and C2 is the path counterclockwise along the circle x2+y2 = 18 from (3,3) to (-3, -3)

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Answer 1

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