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The Calculus Lifesaver by Adrian Banner

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CHAPTER 15 _____________________________

Introduction to Integration

So far as calculus is concerned, differentiation is only half the story. The other half concerns integration. This powerful tool enables us to find areas of curved regions, volumes of solids, and distances traveled by objects moving at variable speeds. In this chapter, we’ll spend some time developing the theory we need to define the definite integral. Then, in the next chapter, we’ll give the definition and see how to apply it. So here’s the plan for the preliminaries on integration:

• sigma notation and telescoping sums;

• the relationship between displacement and area; and

• using partitions to find areas.

15.1 Sigma Notation

Consider the sum

This is not just a sum of random ...

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