Two young mathematicians discuss whether integrals are defined properly.
- Riley, I like integrals.
- I feel fancy when I make an integral sign.
- I know! An integral computes the signed area between a curve and the -axis. But why signed area? Maybe we should just compute plain old area.
- Makes sense to me!
- Unless…maybe there are other applications where ‘‘signed’’ area makes more sense.
One really great way to think about integrals is that they ‘‘accumulate rates.’’