Let S be the surface shown in the following figure in the first octant in the xy-plane, and let F(vector) be a continuously differentiable vector field on R ³ such that ∇ x F-2k̂ on S. If the circulation of F(vector) is 12π around C _­2 , 15π around C ₃ and 14π around C ₄ , determine the circulation of F(vector) around C1 Assume that the radii of C ₂ , C ₃ and C ₄ are My Notes equal to 1.)

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C, C4 х C, C4 х