A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is filled with 40 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 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_i* as x_i.)

express it as an integral

evaluate the integral