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** = bz

**i** - mg

**k** as it travels along the track. The position vector

__r__ = x

__i__ + y

__j__ + z

__k__. By evaluating the line integral

INTEGRAL:

__F__.

__dr__

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.