The vector fieldF= (x + z)i+ zj+ (x = y)kis conservative.

(a) Use the definition of the line integral to evaluate ∫F∙ dralong the pathr(t) = ti+ t2j+ t3kfor 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).