c) A monorail arch spans the dome, running above the line y = 0, i.e. along the path z = 1 - x^2. A train with mass m experiences a force, due to gravity plus an applied electric field, of F
as it travels along the track. The position vector r
. By evaluating the line integral
along the path from the base of the dome at x = -1 to the top of the dome, calculate the work done against F
in driving a train along this distance.
Even just some simple guidance would be appreciated.