so i know that when there is a cable hanging from say a building that is taller than the length of the cable and you want to find the work done lifting half of the cable, you have to split the integral up since each "small piece" of rope in the first half gets lifted up a variable amount while each "small piece" of rope in the 2nd half gets lifted the same amount. 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?