Length of the rope is  ft.

Rope weighs  lb/ft.

Force exerted by the rope to lift it by  ft is  lb.

(a)

Find the work done in pulling the rope to the top of the building.

Therefore, .

Work done as a Riemann sum is  .

 lb-ft.

Work done required is  lb-ft.

(b)

Find the work done in pulling half the rope to the top of the building.

Therefore, .

Set up the distance function for  ft of the rope pulled up.

Total length of the rope is  ft.

Distance function is  ft.

Work done as a Riemann sum is  .

Work done required is  lb-ft. 

(a) Work done required is  lb-ft.

(b) Work done required is  lb-ft.