Consider F and C below.
F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 15z2

k

C: x = t2, y = t + 1, z = 3t − 1, 0 ≤ t ≤ 1
(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.