Consider F and C below.
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.