Education Technology

TI-89 Riemann Sum Activities for Calculus

Published on 07/30/2005

Activity Overview

In this Computer Algebra System (CAS) activity students use Riemann sums to estimate the distance traveled on a trip at various speeds. They utilize the concept of Riemann sums to calculate the area under a curve. Students find limits of Riemann sums, and also convert Riemann sum limits to definite integrals, and vice versa.

Before the Activity

  • Load the Area program on the calculator
  • Install TI Connect™ using the TI connectivity cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 8 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • As an introduction to Riemann sums, find the total distance traveled for a period of time from the provided data

  • Enter the function on the calculator and graph it
  • Find the area between the curve and x-axis in a given range
  • Slice the region vertically and draw rectangles whose left endpoints are on the curves
  • Run the Area program and compare the area of the rectangles with the actual area
  • Use the Trapezoidal Rule to average the results
  • Compare the midpoint sums with the results from the calculator
  • Understand that the weighted average is actually Simpson's rule

  • Sketch the region between the x-axis and the function over a given range
  • Partition the interval into n subintervals
  • Find the expression for the area of the i-th rectangle
  • Evaluate the limit of the Riemann sum
  • Find the area of a plane region bounded by a non-negative function and the x-axis on a closed interval

  • Evaluate a definite integral and find the corresponding Riemann Sum
  • Evaluate the limit and verify the Riemann sum
  • Translate between definite integrals and Riemann sums, and vice versa
  • 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