This applet provides a visual representation of various techniques of numerical integration including left rectangle, right rectangle, midpoint, Simpsons, and trapezoidal. Quadrature area is also given.
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:
Simulation
Technical Requirements:
Applet was written on a Mac using JAVA. Runs well using Windows using Explorer, and UNIX. User may experience difficulties when using Netscape.
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
Content Quality
Rating:
Strengths:
Numerical integration methods include left rectangle, right rectangle, midpoint, Simpsons, and trapezoidal. The user has the option of plotting the graph of the numeric antiderivative as well as plotting the graph of a formula that is the user?s guess of the antiderivative. The graphics are very distinct, with colors effectively used to coordinate the graph with its function. The number of partitions are quickly changed by entering a number for the subintervals or doubling the previous number selected. The function and the interval can easily be changed and the values recalculated.
Concerns:
The applet does not respond well in all cases when the limits of integration fall outside the domain of the integrand, sometimes freezing the browser. The spurious axis labels NaN (Not A Number) that appear frequently should be removed. 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
Rating:
Strengths:
The values of the various methods are reported simultaneously. This applet is very effective in comparing the results of the numerical integration methods, both visually and numerically. Area that occurs above the x-axis is yellow and area that is below the x-axis is green.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The number of partitions can be doubled or a new quantity can be selected. A reset button allows the user to return to the original format.The user can manually change both the x and y intervals of the function. The y-intervals also adjust automatically so that the function is visible in the window created by the x-interval. Zoom in and zoom out features are also available.Documentation is superior and includes directions for using correct syntax.The site was designed to make it easy for someone to host the material locally or to use it for making materials of their own. (The source code is available and reasonably well documented. The applet is in a jar archive to make it easy to get to and download.)
Concerns:
None.
Creative Commons:
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