A bucket that weighs 3 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 42 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 x;.) lim Ax Express the work as an integral. 70 Evaluate the integral. ft-lb )dx