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