This applet provides a visual representation of various techniques of numerical integration including right Riemann sum, left Riemann sum and Trapezoidal Rule.
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 by 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.
Target Student Population:
First year calculus students.
Prerequisite Knowledge or Skills:
A discussion of Riemann sums should go along with this applet.
Evaluation and Observation
Numerical integration methods in this applet include right Riemann sum, left Riemann sum and Trapezoidal Rule. Four preset functions with fixed intervals of integration are provided
Numerical integration methods are limited to the three listed above. The addition of Simpson?s Rule, which is commonly treated in Calculus textbooks, would be nice. 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 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.
There are no examples provided where the curve is below the x-axis.
Ease of Use for Both Students and Faculty
The number of subintervals can be quickly increased or decreased by powers of two. A reset button is included. Documentation is adequate considering that the functions and intervals of integration cannot be modified.