Calculus For Dummies, 2nd Edition

Chapter 18

Taming the Infinite with Improper Integrals

In This Chapter

The hospital rule — in case studying calculus makes you ill

Meeting integrals without manners

The paradox of Gabriel’s horn

In Chapter 17, you used down-to-earth integrals to compute some relatively ordinary things like the area between curves, the volumes of 3-D shapes, the lengths of curves, etc. I say these things are down-to-earth because all of them involved finite things — things with a beginning and an end, things (like a bowl-shaped 3-D object) that you could sort of hold in your hand. In this chapter, you enter the twilight zone of integrals that go to infinity. These are fascinating problems that often have surprising results. But first, we have to take care of L’Hôpital’s rule — a handy technique to put into your calculus bag of tricks.

L’Hôpital’s Rule: Calculus for the Sick

L’Hôpital’s rule is a great shortcut for doing limit problems. Remember limits — from way back in Chapters 7 and 8 — like ? By the way, if you’re wondering why I’m showing you this limit shortcut now, it’s because (a) you may need ...