An elevator at the bottom of a 80 foot shaft weighs 1500 pounds.The 80 foot cable that lifts the elevator weighs 400 pounds. Assumethat the cable has uniform weight over its length. Answer thefollowing questions to calculate the work that is done to raise theelevator 50 feet up from the bottom of the shaft. (a) Write aRiemann sum that approximates the work needed to lift the 50 ft upthe shaft. (b) Write and evaluare an integral to calculate the workdone to raise the cable 50 ft up the shaft. (c) What is the totalwork required to lift the cable and elvator 50 ft up the shaft?
