This site contains an interactive tool that allows the user to approximate the value of the integral of a function using Riemann's sums. The user can then change the range of integration, step size, and number of steps to see how these affect the approximation of the integral.
Type of Material:
This site can be used for demonstrations or for individual student practice.
Identify Major Learning Goals:
Develop a better understanding of the concepts of definite integral and different approximation techniques used to find the value of the integral.
Target Student Population:
Students in a Calculus course
Prerequisite Knowledge or Skills:
First semester of Calculus
This module allows the user to explore the definition of the integral of a function. Students can choose different partitions and then approximate the value of the definite integral using either upper or lower Darboux sums. In addition to that, there are other techniques (such as left and right sum approximation, midpoint rule, trapezoid rule, etc.) available to perform approximation. Students have the option to choose an integration technique, small-number addition error, partition size and number, and range of integration. They can then view a graph of the function along with the value of the integral. They can also view the x and y values of the partition that is being used in the approximation.
In case the interval of integration contains points that make the integral improper, applet issues a warning message.
Not included is the expansion of the sum that is being used in the approximation. It would be helpful for students to see this expansion instead of just the values of x and y in the data area. Also, one of the approximations that can be chosen is “Average Sum”. It is unclear what this method is. Better would be to include “Simpson’s Rule” since that is one of the main approximation techniques used in integration.
Potential Effectiveness as a Teaching Tool
The site can be used as a part of in-class demonstration or a self-guided activity. A list of suggested activities with this tool is given under Instructor tab. A set of links to related topics is a big plus.
It would help the students to have links to an explanation of each of the approximation techniques so that they can quickly find the explanation of what they are seeing in the graphs and numerical solutions.
Ease of Use for Both Students and Faculty
A user can starting working with this tool right away by changing input parameters and executing the applet. There is a link to instructions explaining how to print output if necessary. The graph is easy to read, clearly showing the rectangles, partition and curve.
Search by ISBN?
It looks like you have entered an ISBN number. Would you like to search using what you have
entered as an ISBN number?
Searching for Members?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.