Peer Review

Numerical Integration Rules

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Effectiveness:

Ease of Use:

Overview:: This applet provides a visual representation of various techniques of numerical integration including left rectangle, right rectangle, midpoint, Simpson?s, 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:: Simulation
Technical Requirements:: A Java-enabled 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.

Rating:
Strengths:: Numerical integration methods include left rectangle, right rectangle, midpoint, Simpsons, and trapezoidal. The graphics are very distinct, and the partitions are quickly changed by entering a number or doubling the previous number. The value of the error is presented along with the approximated value of the integral.
Concerns:: The function and its interval of integration cannot be changed.

Rating:
Strengths:: The absolute value of the error is reported for each requested partition. This makes it easy to evaluate the effectiveness of changing the number of subintervals, and makes it possible to compare the accuracy of the various methods of integration.
Concerns:: Values of the various methods are not reported simultaneously. While it is possible to compare the accuracy of the various methods of integration, it would be immediately apparent if all values were reported simultaneously.

Rating:
Strengths:: The number of partitions can be easily doubled. The applet effectively redraws the partitions when a new method is selected and the Draw button is activated.
The documentation is clear and simply describes the steps necessary for use.
Concerns:: When changing from one method to another while using Internet Explorer, a partial redrawing is done. The user must select the Draw button to complete the correct partitioning and receive the numerical value. This problem does not appear when using the Netscape browser.