Problem 14E

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A thick cable, 60 ft long and weighing 180 lb, hangs from a winch on a crane. Compute in two different ways the work done if the winch winds up 25 ft of the cable. a Follow the method of Example 4. b Write a function for the weight of the remaining cable after x feet has been wound up by the winch. Estimate the amount of work done when the winch pulls up x ft of cable.

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