Two young mathematicians discuss whether integrals are defined properly.

- Devyn
- Riley, I like integrals.
- Riley
- I feel fancy when I make an integral sign.
- Devyn
- 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. - Riley
- Makes sense to me!
- Deyvn
- 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.’’