Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

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

Reconnoitering rectangles

Totaling up trapezoids

Applying 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.

By the way, much of the material in this chapter and the first section of Chapter 15 is both more ...