Other questions

In the same vein as your bicycle with a speedometer, we present some more situations and questions below. These are not questions with exact answers, nor even the types of questions asked in secondary-school mathematics; but they raise issues about how you might approach them mathematically. How might they also require us to add something up over many short intervals to get close to the exact answer — that is, by using integration? Some of them are contrived and unrealistic, but perhaps they will be useful to think about.

It is the last problem — an area under a graph — which is a purely mathematical one, and the most abstract. However, all of the other situations, it turns out, can be related to this type of mathematical problem. Integration is intimately connected to the area under a graph.

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