This applet provides a visual representation of various techniques of numerical integration including left rectangle, right rectangle, midpoint (circumscribed and inscribed) and trapezoidal.
Please see A Comparison of Numerical Integration Applets in which seven such applets from the MERLOT collection, including this one, are compared with regards to their ease of use, effectiveness, and richness of features. This comparison also contains links to the applets? sites within the MERLOT collection.
Type of Material:
JAVA supported web browser.
Identify Major Learning Goals:
The visual representation of the partitions and the corresponding sum of their areas approximates the area under a curve.
Target Student Population:
First year calculus students.
Prerequisite Knowledge or Skills:
A discussion of Riemann sums should go along with use of this applet
Evaluation and Observation
Numerical integration methods include left rectangle, right rectangle, midpoint, circumscribed rectangle, inscribed rectangle and trapezoid. Five preset functions are provided, including a discontinuous one and one with an infinite limit. The user may create other functions and set the interval of integration.
Simpson?s method is not included. Problems arise whenever limits of integration are chosen outside the domain of the integrand. The addition of an error estimate for each method of integration would facilitate comparison of the accuracy of each method, as well as the effect of changing the number of subintervals.
Potential Effectiveness as a Teaching Tool
The applet is effective in providing a visual representation of the method selected.
The values of the various methods are not reported simultaneously, reducing the applet?s effectiveness as a tool to compare methods of integration. The scale on the x- axis appears arbitrary and does not coordinate with the rectangles drawn. This is confusing to the user who has the impression that these values are important in the numerical integration process.
Ease of Use for Both Students and Faculty
The applet efficiently redraws the subintervals when a new method is selected. An error in syntax results in a message describing the correction necessary.
The maximum and minimum y values are set manually and do not adjust automatically; consequently the function may not be visible in the window created by the x-interval selected. Error messages associated with incorrect syntax are good, but an explanation of allowed syntax would be even better.