A Comparison of Numerical Integration Applets

There are over a dozen learning objects that all can perform numerical integration.  This webpage attempts to assist the instructor or student with locating them, rating them and comparing them.  For each site, you can click on the button to view a popup that gives a description of some of the features and shortcomings of the applet.  A rating system has been established that looks at layout, functionality, ease of use, graphical display, on page information, and links to external resources.  The summary can be found in both summative and tabular format by scrolling down towards the bottom of this page or by clicking on the bookmark links below:

Qualitative Comments on Each Site

A Table Rates Different Qualities of the 14 Numerical Methods Applets

Below is a list of all of the Numerical Integration Applets that Reside on MERLOT

1. Dave Eck,  A Riemann Sums Configurable Applet:  http://math.hws.edu/javamath/config_applets/RiemannSums.html
   
   
2. University of Utah, Finding the Area Under a Curve:   http://www.math.utah.edu/~carlson/teaching/java/calculus/ApproxArea.html
   
   
   
3. Thomas E. Leathrum,  Numerical Integration:  http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/trapsimp.html
   
   
   
4. Nicholas Exner,  Methods for Numerical Integration:   http://www.mste.uiuc.edu/activity/integration/default.html
   
   
   
5. Thomas Downey,  Midpoint and Trapezoidal Riemann Sums:  http://www.calculusapplets.com/midpointtrap.html
   
   
   
6. Donald Kreider and Dwight Lahr,  Numerical Integration:  http://math.dartmouth.edu/~klbooksite/appfolder/tools/NumericalIntegration.html
   
   
   
7. John Wiley & Sons, Numerical Integration Applet:  http://www.wiley.com/college/mat/anton243310/mod2/applet1/applet1.html
   
   
   
8. Peter Maserick, Numerical Integration:  http://www.math.psu.edu/courses/maserick/integration/integ.html
   
   
   
9. Dan Sloughter ,Numerical Integration Rules:  http://math.furman.edu/~dcs/java/NumericalIntegration.html
   
   
   
10.  Joseph Zachary, Numerical Integration Simulation:  http://www2.cs.utah.edu/~zachary/isp/applets/Integrate/Integrate.html
    
    
    
11. Ken Levasseur, Riemann Integration:  http://www.hostsrv.com/webmaa/app1/MSP/webm1010/riemann.msp
    
    
    
12. Mike May, Riemann Sums:  http://www.slu.edu/classes/maymk/Riemann/Riemann.html
    
    
    
13. Miguel Bayona, Riemann Sums:  http://mathplotter.lawrenceville.org/mathplotter/mathPage/riemann.htm
    
    
    
14. Scott Sarra, Riemann Sums Applet:  http://www.scottsarra.org/applets/calculus/RiemannSums.html
    

List of Qualitative Comments on Each Site

(Click on the button to jump to the icon for this site.)  

1. The best site for instructors to imbed the applet directly onto their own web page. No Simpson's Rule or links about the calculus, but very user friendly. 
   
   
2. This is just a demo of y = x².  Very limited in functionality. 
   
   
3. Takes a long time to load, Shades the region, but not the approximation. 
   
   
4. Graph very limited.  No control of viewing rectangle and no shading given. 
   
   
5. Very easy to use and graphics including the shading of the approximation is clear.  Gives all approximations except Simpson's.  Uses a slider or input to change a and b. 
   
   
6. Contains all the elementary approximation techniques.  The graph is very responsive and allowing for clear visualization.  It took some time to learn how to resize the viewing rectangle.  Click to zoom out and construct a rectangle with the mouse to zoom in.  No external links given. 
   
   
7. Easy to use, but no internal or external help.  Will only work if students know how to enter in functions.  Graphics include shading and most approximations are provided. 
   
   
8. Very basic and limited to just 4 predefined functions.  The rectangles are outlined but not shaded in.  There is a help button, but nothing to explain the underlying mathematics. 
   
   
9. This only contain a single approximation. The shading does not contain outlines, so the rectangles or trapezoids are difficult to visualize. 
   
   
10. This applet contain a choice of 12 pre-defined functions.  The screen usually needs to be refreshed for the results to show clearly.  Outlines of the rectangles are given but they are not shaded in.  The menu driven File, Help, Method, and Function choices are easy to navigate. 
    
    
11. Has user input of functions, but there is no help on how to input functions.  Some of the syntax of this input is not natural and it is not obvious when a mistake is made.  This is the only applet that demonstrates random intervals and random choices of each x-value. 
    
    
12. This one has it all.  User input of function, predefined functions, graphical interface with shading, links for help, all the typical approximations, and even a worksheet. 
    
    
13. This site uses Geogebra.  It contains all the functionality, user defined functions, sliders that allow for changing the coefficients of the function and the number of partitions.  The endpoints can be dragged.  The only thing missing is the supporting information or links that explain the calculus. 
    
    
14. This site has predefined functions and user input functions.  It is easy to use and the graphics are straightforward.  No Simpson's Rule capability. 

A Table Rates Different Qualities of the 14 Numerical Methods Applets

GS = Graphical Support

CSM = Complete Set of Methods

OSSI = On Site Supporting Info

EL = External Links

UDFV = User Defined Functions and Values

CADI = Click and Drag Interface

LAV = Labeled Axes (values)

ETII = Easy to Input Info

CO = Clear Output

Questions Comments Suggestions

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