Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics V / 2 / b / ii / Solution

Compute the line integral on each straight segment. On the first, $y=z=0$ and only $dx$ contributes; on the second, $x=1,z=0$ and only $dy$ contributes; on the third, $x=y=1$ and only $dz$ contributes. ThereforeAlthough $F_x=9$ on the second segment, that term does no work there because $dx=0$.