Question: Let F =(F1, F2) be a continuously differentiable vector field on the region D given by the plane R2 with the origin (0, 0) taken

Let F =(F1, F2) be a continuously differentiable vector field on the region D given by the plane R2 with the origin (0, 0) taken away. Assume that F satisfies OF2 _ OF1 Ox dy Let Ca be the circle of radius a centred at the origin, oriented counterclockwise. Show that / Ca F . di = K for some constant K independent of a

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