Consider F and C below.

Question

F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 15z2

k

C: x = t2, y = t + 2, z = 3t − 1, 0 ≤ t ≤ 1
(a) Find a function f such that F = ∇f.
f(x, y, z) =
x2z+xy2+5z3+C
Correct: Your answer is correct.

(b) Use part (a) to evaluate
C
∇f · dr
along the given curve C.

Answer 1

∇f · dr = 2t3 + (t+2)2(3t-1) + t4 + 15(3t-1)2 = 24t3 - 18t2 + 8t + 15
Correct: Your answer is correct.