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now when you are finding the work done by pumping water, lets say the problem is to find the work done in pumping water out of the top of the container so that only a depth of 1 ft of water remains. would you have to split up the integral in a similar way to the cable problem described above? or could you just adjust the limits of integration accordingly. for example if the tank is 4 ft tall and the limits to find the work to pump out all the water is from 0 to 4. could you change it so that the limits become from 0 to 3 to find the work needed to pump the water out so that 1ft depth remains?