The vector field F = (x + z)i + zj + (x = y)k is conservative.
(a) Use the definition of the line integral to evaluate ∫F ∙ dr along the path r(t) = ti + t2j + t3k for 0 ≤ t ≤ 1. The goal here is to carry out the full calculation, rather than using the fundamental theorem for line integrals).
(b) Find a corresponding potential function f(x,y,z) such that Ñf = F.
(c) Use the result calculated in (b) to re-evaluate the integral in (a).