This applet provides a visual representation of various techniques of numerical integration including right rectangle, midpoint, 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 and tutorial
Technical Requirements:
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 the curve. The exact value is also given and compared to the calculated value.
Target Student Population:
First year calculus students.
Prerequisite Knowledge or Skills:
A discussion of Riemann sums should go along with this applet.
Content Quality
Rating:
Strengths:
Numerical integration methods in this applet include right rectangle, midpoint and trapezoid. The exact value is also provided. The difference and percent difference between the Riemann sum and the exact value are given. A pie graph of the difference allows the user to visually determine if the value of the numerical method has improved with increased rectangles or change of method. Twelve preset functions are provided.
Concerns:
Numerical integration methods are limited to the three listed above. The addition of Simpson?s Rule, commonly covered in Calculus textbooks, would be nice.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This applet?s strength is in the comparison of the calculated method with the exact value and the visual representation of this difference in a pie graph.
Concerns:
The values of the various methods are not reported simultaneously, reducing the applets effectiveness as a tool to compare methods of integration.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The interval of integration is initially set between ?7 and 7. As the user uses the mouse to drag the limits of integration, the subintervals and the calculated error adjust, as well as the pie graph for error. The applet intelligently restricts limits of integration to values within the domain of the chosen function. The number of partitions can be increased or decreased by one or by 10. The help menu is well done, and the documentation on the associated web page provides an explanation and example of what is to be done with the applet.
Concerns:
None.
Creative Commons:
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