Question: O 2 3 X 12-18 (a) Find a function f such that F = Vf and (b) use d. part (a) to evaluate Jc F

O 2 3 X 12-18 (a) Find a function f such that F = Vf and (b) use d. part (a) to evaluate Jc F . dr along the given curve C. 12. F(x, y) = (3 + 2xy2) i + 2x2y j, C is the arc of the hyperbola y = 1/ x from (1, 1) to (4, !) 13. / F(x, y) = x2y'itx'yzj, C: r(t) = (+3 - 2t, 13 + 2t), Ost = 1 14. F(x, y) = ( 1 + xy )exy i + x exy j, C: r(t) = costi + 2 sintj, Ost= 1/2 15. F(x, y, z) = yz i + xz j + (xy + 2z) k, C is the line segment from (1. 0. -2) to (4. 6, 3)

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