MA 3972-MA-Book April 11, 2018 16:1CHAPTER
13
Big Idea 3: Integrals and the
Fundamental Theorems of Calculus
Areas and Volumes
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 area under a curve and the volume
of a solid. Some of the techniques that you will be shown include finding 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 Method270