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Question: problem 8 let c be a smooth curve parametrized by...

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Problem 8: Let C be a smooth curve parametrized by 7(t) = (cos sint sint, sin sint sint, cost), t E [O, 2 Then, the curve C is a closed curve on S2 and divide S2 into two parts. Let Σ denote the part with smaller area. Assume that a vector field F is F(z, y, z) (y,-z0) N is the unit normal vector field on Σ and T is the tangent vector field on such that T is compatiable with N (which means that TzN points away from SJ. (a) Evaluate Jas F. (TrN) ds without using Divergence Theorem on surfaces. (b) Evaluate div FdS without using Divergence Theorem on surfaces.

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