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 cableSee 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