Education Technology

Integral Calculus

Published on 06/09/2008

Activity Overview

In this activity, students use various features of the calculator to investigate some of the fundamental concepts of integral calculus. They study Riemann Sums and explore limitations of numerical integration.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 79 - 90 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.
    Follow the Activity procedures:
    Riemann Sums:

  • Use the Sum and Seq commands to compute the Riemann sums of a function over a given interval

  • Compute the Midpoint, Trapezoid, and Simpson approximations
  • Verify the results using the NINT program
  • Use the fnInt command for the numerical approximation of Riemann Integrals
  • Study the short-cut method which expedites the process of calculating more than one integral

  • Average Value of a Function:
  • Use the AVGF program, and the rand command to generate random numbers on the calculator and determine the average value of a function

  • Graphing Integrals with Variable Upper Limits:
  • Graph an integral function with a variable upper limit, and evaluate it for specific values in the interval
  • Verify graphically that the derivative of an integral function is the function itself

  • Limitations of Numerical Integration:
  • Integrate an exponential function over different intervals
  • Observe that when the limit tends to zero the evaluated values are incorrect
  • Integrate a step function after setting tolerance levels
  • Observe that value of the function is zero in certain intervals
  • After the Activity

    Students complete the exercises on the Activity sheet.
    Review student results:

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