Using the Integral to Solve Problems
IN THIS CHAPTER
Adding up the area between curves
Figuring out volumes of weird shapes
Finding arc length
As I say in Chapter 8, integration is basically adding up small pieces of something to get the total for the whole thing — really small pieces, actually, infinitely small pieces. Thus, the integral
tells you to add up all the little pieces of distance traveled during the 15-second interval from 5 to 20 seconds to get the total distance traveled during that interval. In all problems, the little piece after the integration symbol is always an expression in x (or other variable). For the above integral, for instance, the little piece of distance might be given by, say, . Then the definite integral
would give you the total distance traveled. Your main challenge in this chapter is simply to come up with the algebraic expression for the ...