A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter x,* as x₁.) lim n→∞ i=1 Ax Express the work as an integral. Evaluate the integral. ft-lb

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