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Partitions give us a grip on a process. We then obtain answers by doing a living recombination of a partition. By a ‘living’ recombination is meant one allowing the partition valuation to vary. For example, we can partition distance of travel into rate times time: D = RT. Since R = D/T, we have D = (D/T)T, but (D/T) is speed, which can vary. The living recombination is called ‘integration’, and integrating speed over time gives distance of travel. For example, traveling at a constant speed of 20 kilometers per hour for 3 hours gives a distance of travel of 60 kilometers. Significantly, if the speed over the 3 hours is not constant, but has an average of 20 kilometers per hour, the distance of travel is the same as before: 60 kilometers. In general, the distance of travel is the area under the speed curve, between the two points in time under consideration.
keywords: Mathematics, Calculus, instantaneous rate of change