A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep.

A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 36 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done W in pulling the bucket to the top of the well.Approximate the required work by a Riemann sum.

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