Mathematics

Mathematics

Problem

(a) Find a function ff such that F=∇f\mathbf{F} = \nabla f and (b) use part (a) to evaluate ∫CF⋅dr\int_C \mathbf{F} \cdot d\mathbf{r} along the given curve CC. F(x,y,z)=2xyi+(x2+2yz)j+y2k\mathbf{F}(x, y, z) = 2xy\mathbf{i} + (x^2 + 2yz)\mathbf{j} + y^2\mathbf{k}, CC is the line segment from (2,−3,1)(2, -3, 1) to (−5,1,2)(-5, 1, 2) a. Find a function ff such that F=∇f\mathbf{F} = \nabla f. b. Use part (a) to evaluate ∫CF⋅dr\int_C \mathbf{F} \cdot d\mathbf{r} along the given curve CC.

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