Chapter 14

# Intro to Integration and Approximating Area

In This Chapter

Integrating — adding it all up

Approximating areas and sizing up sigma sums

Using the definite integral to get exact areas

Totaling up trapezoids

Simpson’s rule: Calculus for Bart and Homer

Since you’re still reading this book, I presume that means you survived differentiation (Chapters 9 through 13). Now you begin the second major topic in calculus: integration. Just as two simple ideas lie at the heart of differentiation — *rate* (like *miles per hour*) and the steepness or *slope* of a curve — integration can also be understood in terms of two simple ideas — *adding up* small pieces of something and the *area* under a curve. In this chapter, I introduce you to these two fundamental concepts.

## Integration: Just Fancy Addition

Consider the lamp on the left in Figure 14-1. Say you want to determine the volume of the lamp’s base. Why would you want to do that? Beats me. Anyway, a formula for the volume of such a weird shape ...