AP-Calculus-BC 2727-MA-Book May 11, 2018 14:18CHAPTER 12
Big Idea 3: Integrals and the
Fundamental Theorems of Calculus
Areas, Volumes,
and Arc Lengths
IN THIS CHAPTER
Summary:In this chapter, you will be introduced to several important applications of
the definite integral. You will learn how to find the length of a curve, the area under a
curve, and the volume of a solid. Some of the techniques that you will be shown
include finding the area under a curve by using rectangular and trapezoidal
approximations, and finding the volume of a solid using cross sections, discs, and
washers. These techniques involve working with algebraic expressions and lengthy
computations. It is important that you work carefully through the practice problems
provided in the chapter and check your solutions with the given explanations.
Key Ideas
KEY IDEA !The functionF(x) =∫x
af(t)dt
!Rectangular Approximations
!Trapezoidal Approximations
!Area Under a Curve
!Area Between Two Curves
!Solids with Known Cross Sections
!The Disc Method
!The Washer Method
!Area and Arc Length for Parametric and Polar Curves
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