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Consider the following line integral of the conservative vector field: ZC(y2 sinz−z)dx + 2xy sinz dy...

Consider the following line integral of the conservative vector field: ZC(y2 sinz−z)dx + 2xy sinz dy + (xy2 cosz−x)dz where C is the contour given by r(t) = ht3,2t2 −1,πti, 0 ≤ t ≤ 1/2. a. [4] Find the potential f of the vector field satisfying the condition f(1,1,0) = 0. b. [5] Compute the line integral.

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