Applications of Intergration (Work related)

1. A heavy rope, 50ft long, weights 0.5 lb/ft and hangs over the edge of a building 120 ft high.

a) How much work is done in pulling the rope to the top of the building?

b) How much work is done in pulling half the rope to the top of the building?

My solution:

Work = Force x Distance

W = $\displaystyle \int Fxdx$

Force = (Density) = (0.5)

So Fx = 0.5x

Then: $\displaystyle \int_{0}^{50} 0.5 x dx $

Is that correct?

I have no idea how to do the b part.

Thank you!

P.S. How come I can't do the upper and lower limit of defined intergration? I used \int^50_0 and it didn't work.