# Activities

• • • ##### Subject Area

• Math: Algebra I: Expressions
• Math: Algebra I: Functions and Relations

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

## TI-89 Riemann Sum Activities for Calculus

#### 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.

• 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