MA101: Single-Variable Calculus I

8.1: The Area between Curves

• Suppose you want to find the area between two concentric circles. How would you do this? Logic dictates that you subtract the area of the smaller circle from that of the larger circle. As this subunit will demonstrate, this method also works when you are trying to determine the area between curves.
  

• University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 4: Integration, Section 4.5: Areas between Two Curves" URL

  Read Section 4.5 (pages 218 through 222).
  

• Massachusetts Institute of Technology: David Jerison's "Applications of Logarithms and Geometry" Page

  Watch this lecture from 21:30 to the end. In this lecture, Dr. Jerison will explain how to calculate the area between two curves.
  

• Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web" URL

  Click the "Index" button for Book II. Scroll down to "2. Applications of Integration," and click button 115 (Area between Curves I). Work on problems 6-13. Next, choose button 116 (Area between Curves II), and complete problems 4-10. If at any time a problem set seems too easy for you, feel free to move on.
  

• Indiana University Southeast: Margaret Ehringe's "Section 5.3 Area between Two Curves" URL

  Work on problems 1-3 and 6-9. When you have finished, scroll down to the bottom of the page; the answers to the problems are printed upside-down at the end of the exercises.

  The point of this third assignment is for you to practice setting up and completing these problems without the graphical aids provided by the Temple University media; you will have to graph these curves for yourself in order to begin the problems.