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
Content Quality
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 for the subintervals or by changing the integration method. The function and the interval can easily be changed and the values recalculated.
Concerns:
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. The applet does not respond well over intervals on which the integrand is undefinded. For example, an attempt to integrate log(x) using the interval from ?1 to 20 resulted in poor graphics and incomplete results reported.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The values of the various methods are reported simultaneously, and the one whose partitioning is shown is given in red font. This applet is very effective in comparing the results of the numerical integration methods, both visually and numerically.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet very quickly changes the partitions as the user clicks on different numerical integration methods. The applet also reports any errors in syntax. The maximum and minimum y values adjust automatically so that the function is visible in the window created by the x-interval selected.
Concerns:
No documentation is available to help with syntax errors. The user must be aware of syntax appropriate for a calculator or software. For example, the square root function is entered as sqrt(x).
Creative Commons:
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