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The Calculus Lifesaver by Adrian Banner

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CHAPTER 29 _____________________________

Volumes, Arc Lengths, and Surface Areas

We have used definite integrals to find areas. Now we’re going to use them to find volumes, lengths of curves, and surface areas. For volumes and surface areas, we’ll pay special attention to solids which are formed by revolving a region in the plane about some axis which lies in the plane; such solids are called solids of revolution. In the case of volumes, we’ll also look at some more general solids. Here, then, is the game plan for this chapter:

• finding volumes of solids of revolution using the disc and shell methods;

• finding volumes of more general solids;

• finding arc lengths of smooth curves and speeds of parametric particles; and

• finding surface areas ...

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