Forget Dr. Phil: Use the Integral to Solve Problems
In This Chapter
One mean theorem: “Random acts of kindness!? Don’t make me laugh.”
Adding up the area between curves
Figuring out volumes of odd shapes with the deli meat method
Mastering the disk and washer methods
Finding arc length and surface area
As I say in Chapter 14, integration is basically just 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 some other variable). For the above integral, for instance, the little piece of distance might be given by, ...