Section Summary

In this section we have begun to consider antidifferentiation, the inverse operation to differentiation. As we noted in the introduction to this chapter, finding antiderivatives for `ftext[(]t text[)]` is the same as finding solutions to the differential equation

So, it is not surprising that each function has infinitely many antiderivatives — all differing by a constant.

Our differentiation rules — the Constant Multiple Rule, the Sum Rule, and, most importantly, the Chain Rule — enable us to extend our elementary antidifferentiation formulas to a much wider collection of functions.

We are far from done with the calculation of antiderivatives. In fact, this will be a thread running through Chapters 6-10. In particular, in Chapter 8 we will take up the use of the Product Rule in calculating antiderivatives, which turns out to be a more subtle issue than the ones we consider in this chapter.