Our new interpretation of the definite integral is very useful. It shows us how to turn a lot of different problems into integration problems. We introduced it in the context of finding areas, but it is vastly more general than that. Almost anything that comes into the category of `break it into small bits, approximate on the bits and then add up the bits' yields a definite integral of some form.
In this section I will look at a few applications. You may meet others in other subjects.