1. The problem statement, all variables and given/known data A freight elevator weighing 3000 pounds is supported by a 12 foot long cable that weighs 14 pounds per linear foot. Approximate the work required to lift the elevator 9 feet by winding the cable onto a winch 2. Relevant equations W = int(f)dy 3. The attempt at a solution The work lifting the elevator is 3000lb(9ft)=27000ft*lb The winch is lifting a piece of rope dy a distance 12-y from 0 to 9 Each section dy weighs 14dy (sorry for the lack of latex) W = int0-9[14(12-y)]dy = 14int0-9[(12-y)]dy W = 14[12y-.5y2]0-9 W = 945 ft*lb Total work = 27000+945 = 27,945ft*lb But the book has an answer of 36,945. The 945 leads me to think I set up the integral correctly, but where did the extra 900 come from?