Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a function f such that F = ∇f. f(x, y, z) = Correct: Your answer is correct. (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Required solution (a) (b) 40.

Step-by-step explanation:

Given,

(a) Let,

Then,

Integrating we get,

Differentiate this with respect to y we get,

compairinfg with of the given function we get,

Then,

Again differentiate with respect to z we get,

on compairing we get,

  (By integrating h'(z))  where C is integration constant. Hence,

(b) Next, to find the itegration,

your answer would be 12