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