A bucket begins weighing 30 pounds, including the sand it holds. The bucket is to be lifted to the top of a 25 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.1 pounds of sand each foot it is lifted.

Question

Find the work done lifting the bucket to the top of the building.

Answer 1

work = force * distance, so

∫[0,25] 30-.1x dx