[ P rev | Main | Next ]

Improper Applet

Improper is used to display concepts related to improper integrals. It shows the graph of the integrand and colors in the area under the curve between the lower and upper limit (using red for negative area and green for positive area). To handle large values of the upper limit, or values increasingly close to a vertical asymptote, the applet provides a table with six rows, each representing the value of the integral for a different upper limit. You can set these to be increasing large numbers when illustrating an improper integral with an upper limit of infinity, or you can set these to approach a given value where the integrand has a vertical asymptote. Be careful of setting the b values to very large numbers, as the applet may take a long time to recompute the value of the integral.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.Improper" codebase="../../assets"
archive="webcompmath.jar,calculus.jar" height="400" width="640">
<param name="UseLoadButton" value="no" />
<param name="Example1" value="1. x;x;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example2" value="2. x^2;x^2;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example3" value="3. 1/x^2;1/x^2;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example4" value="4. 1/x^3;1/x^3;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example5" value="5. 1/x^0.5;1/x^0.5;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example6" value="6. 1/x;1/x;1;5;-1,6,-5,5;5,10,50,100,500,1000;false" />
<param name="Example7" value="7. 1/(2-x)^0.5;1/(2-x)^0.5;1;2;-1,3,-5,5;1.5,1.9,1.99,1.999,1.9999,1.99999;false" />
<param name="Example8" value="8. 1/(2-x)^2;1/(2-x)^2;1;2;-1,3,-5,5;1.5,1.9,1.99,1.999,1.9999,1.99999;false" />
<param name="Example9" value="9. Your turn!;1/x^2;1;5;-1,6,-5,5;5,10,50,100,500,1000;true" />

This applet takes the following parameters:

Param Name Type Default Description
Example1, ... String N/A Each example is a list of strings separated by semicolons. The strings, in order, are:
1. The name of the example, displayed in the example menu.
2. The expression for the integrand function f(x).
3. The value for a, the lower limit.
4. The value for b, the upper limit.
5. The xmin, xmax, ymin and ymax values for both graphs, separated by commas.
6. A list of up to six comma-separated numbers to be used as the b values in the table.
7. Whether or not the user can edit the b values in the table. "true" means the values are editable, "false" means they are not.

[ Prev | Main | Next ]