Education Technology

Above and Beyond

Published on 08/02/2005

Activity Overview

In this Computer Algebra System (CAS) activity, students create a general solution for calculating the ratio of the areas above and below a curve.

Before the Activity

  • Install TI Connect™ using the TI connectivity cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 2 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Plot the lines y = x, y = 1, and x = 1
  • Form a square using segments on the lines y = 1 and x = 1
  • Evaluate the ratio of the area of the triangle above the y = x line to the area of the triangle below the y = x line
  • Notice that the ratio is 1 : 1


  • Plot the curves y = x2, y = 1, and x = 1
  • Evaluate the areas above and below the curve by integrating them numerically
  • Note that the ratio of the areas is 2 : 1


  • Understand that if the index of x in the curve is n, then the ratio of the areas of the curves will be n : 1
  • Realize that if the index of x is a negative integer, there is no area enclosed under the graph in the specified interval
  • Repeat the problem with different values of n over various intervals


  • Use CAS to explore the two areas
  • After the Activity

    Students' answer questions on the Activity sheet.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary