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Revolution Applet

Revolution illustrates volumes of revolution. It shows an upper and lower function, shades in the area between them and bounded by the upper and lower limits. It also shows the axis of revolution and a disc/washer that represents one slice of the Riemann sum. The slice is moveable by the user. A lightly colored slice is also shown at each end of the volume to help the user visualize the shape.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.Revolution" codebase="../../assets"
archive="webcompmath.jar,calculus.jar" height="400" width="400">
<param name="UseLoadButton" value="no" />
<param name="Example1" value="1. Simple Cylinder;2;0;0;1;0;2;false;false;-1,3,-3,3;5" />
<param name="Example2" value="2. Cone;x;0;0;1;0;2;false;false;-1,3,-3,3;5" />
<param name="Example3" value="3. Revolving a Parabola;x^2;0;0;1;0;2;false;false;-1,3,-4,4;5" />
<param name="Example4" value="4. Cylinder with a hole;2;1;0;1;0;2;false;false;-1,3,-3,3;5" />
<param name="Example5" value="5. Cylinder with a cone-chaped hole;2;x;0;1;0;2;false;false;-1,3,-3,3;5" />
<param name="Example6" value="6. Odd shape;x;x^2;0;0.5;0;1;false;false;-0.5,1.5,-1.5,1.5;5" />
<param name="Example7" value="7. Odd shape, R and r swapped;x;x^2;0;1.5;1;2;false;false;0,2.5,-4,4;5" />
<param name="Example8" value="8. Odd shape with new axis;x;x^2;1;0.5;0;1;false;false;-0.5,1.5,0,2;5" />
<param name="Example9" value="9. Odd shape with vertical axis;y;sqrt(y);0;0.5;0;1;true;false;-1,1,-0.5,1.5;5" />
<param name="Example10" value="10. You try!;x^2;0;0;1;0;2;false;true;-1,3,-4,4;5" />

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 f(x), the upper function.
3. The definition for g(x), the lower function.
4. The location of the axis of revolution.
5. The value for x, which controls the location of the slice to be displayed.
6. The value for a, the lower limit.
7. The value for b, the upper limit.
8. Whether to use vertical or horizontal slices. Use "true" for horizontal slices and to interpret the functions as f(y) and g(y); use "false" for vertical slices and to interpret the functions as f(x) and g(x).
9. Whether to show the inverse check box. Use "false" to hide the check box, "true" to show the check box.
10. The xmin, xmax, ymin, and ymax for the graph, as a comma-separated list of numbers.
11. The width of the slice, in pixels.

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