Finding the work done

Question

a heavy rope 60 ft long weighs 0.7 lb/ft and hangs over the building 130 ft high.

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

Show how to approximate the required work by a Riemann sum.

Express the work as an integral. 

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

I have part a mostly but I keep getting part b wrong. I know that it is the integral from 0 to 30.

Answer 1

I think the amount of work in part a is just the integral of s(60-s) ds between 0 and 60.