Activity Overview
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
Re-teach concepts as necessary