This applet provides a visual representation of numerical integration using the midpoint rectangle method.
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 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.
Content Quality
Rating:
Strengths:
For appropriately chosen integrands, this applet clearly demonstrates the concept of area under a curve as the limit of Riemann sums. Documentation is good, and an activity is suggested.
Concerns:
The size of the viewing window is fixed. It is easy to choose a function with graph outside the window, leading to confusing results. Integrands are limited to polynomials of degree three. No error is reported, and only one technique of numerical integration is available (midpoint rectangle).
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This applet would be effective for a classroom demonstration of the basic concept of limits of Riemann sums.
Concerns:
There is not enough flexibility in choice of method of integration, integrand, or limits of integration to allow for student experimentation. The ease of choosing functions with graphs outside the viewing window would lead to many confusing situations for students. The restriction to one method of integration prevents a comparative study of methods, and the lack of an error report gives no quantitative way to judge the effectiveness of the one method of integration available.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
It is very easy to choose the coefficents of the polynomial of degree three used for the integrand. Increasing the number of subintervals in the partition is accomplished with a single buttion click.
Concerns:
The ease of choosing functions with graphs outside the viewing window would lead to many confusing situations for students.
Creative Commons:
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