A chain 180 meters long hangs over the edge of a building that is 180 meters tall. The chain weighs 25 newtons per meter. There is a bucket at the end of the chain resting on the ground. Initially the bucket and the water it contains weigh 4000 newtons. As the bucket is lifted water leaks from the bucket at a rate of 20 newtons per meter that the bucket is lifted. Setup, but do not evaluate, an integral that gives the amount of work done in lifting the bucket and chain from the point where the chain 150 meters long to the point where the chain is 50 meters long. The amount of work done is 490, 000 J.

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