Show how to approximate the required work by a Riemannsum. Then express the work as an integral and evaluate it. A bucket that weighs 4 lb and a rope of negligible weightare used to draw water from a well that is 80 ft deep. Thebucket is filled with 40 lb of water and is pulled up at a rateof  2ft/s , but water leaks out of a hole in the bucket at a rateof 0.2lb/s . Find the work done in pulling the bucket to thetop of the well.

Show how to approximate the required work by a Riemann
sum. Then express the work as an integral and evaluate it.

A bucket that weighs 4 lb and a rope of negligible weight
are used to draw water from a well that is 80 ft deep. The
bucket is filled with 40 lb of water and is pulled up at a rate
of  2ft/s , but water leaks out of a hole in the bucket at a rate
of 0.2lb/s . Find the work done in pulling the bucket to the
top of the well.