Definite Integrals

Now it’s time to get some facts straight about definite integrals. First we’ll give an informal definition in terms of areas; then we’ll use our ideas about partitions from the previous chapter to tighten up the definition. After one (exhausting) example of applying the tightened-up definition, we’ll see what else we can say about definite integrals. More precisely, we’ll look at the following topics:

• signed areas and definite integrals;

• the definition of the definite integral;

• an example using this definition;

• basic properties of definite integrals;

• using integrals to find unsigned areas, the area between two curves, and areas between a curve and the *y*-axis;

• estimating definite ...

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