A fireman is holding one end of a rope at the top of a building that is 100 ft high. The rope weighs 1 lb/ft and is 200 ft long. Note that 100 ft of the rope is just lying on the ground freely. What is the total amount of work done in pulling all of the rope up to the top of the building? Hint: The total amount of work is the sum of two definite integrals - one for the first 100 ft of the rope, and another one for the last 100 ft of the rope. Note that for the last 100 ft of the rope, each differential segment has to traverse a distance of 100 ft.