Chapter 17

Forget Dr. Phil: Use the Integral to Solve Problems

In This Chapter

arrow One mean theorem: “Random acts of kindness!? Don’t make me laugh.”

arrow Adding up the area between curves

arrow Figuring out volumes of odd shapes with the deli meat method

arrow Mastering the disk and washer methods

arrow 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, ...

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