Summary of Approximating Integrals

Throughout most of our calculus journey, we’ll be given functions that have nice, closed-form antiderivatives in terms of elementary functions. This is really the only way we can learn the very useful integration techniques we have been and will be taught. However, the real world is messy. If you end up integrating a function while working in it, odds are that it will have no closed-form antiderivative and you will do so numerically using approximations, as we’ve learned in this section. But remember that by providing bounds and thinking critically about maximum error, even approximations can be extremely useful.