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 ...