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Area Applet

Area is used to show how a Riemann sum consisting of the areas of rectangles can be used to approximate the area under a curve or between two curves. The applet supports regular functions with vertical rectangles, or inverse relations with horizontal rectangles. The area is colored in yellow for both positive and negative area. There is also a representative rectangle that can be moved by the user.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.Area" codebase="../../assets"
archive="webcompmath.jar,calculus.jar" height="400" width="400">
<param name="UseLoadButton" value="no" />
<param name="Example1" value="1. Vertical Slices of a line;x;0;1;0;2;false;false;-3,3,-3,3" />
<param name="Example2" value="2. Vertical Slices of a line;-x;0;1;0;2;false;false;-3,3,-3,3" />
<param name="Example3" value="3. Vertical Slices of a cubic;x^3;0;1;-2;2;false;false;-3,3,-10,10" />
<param name="Example4" value="4. Vertical Slices between line and parabola;x;x^2;0.5;0;1;false;false;-.25,1.25,-.25,1.25" />
<param name="Example5" value="5. Vertical Slices between line and parabola;x;x^2;1.5;1;2;false;false;0,3,0,5" />
<param name="Example6" value="6. Vertical Slices of a parabola;1;x^2;0.5;0;1;false;false;-.5,1.5,-.5,1.5" />
<param name="Example7" value="7. Horizontal slices;0;sqrt(y);0.5;0;1;true;false;-.5,1.5,-.5,1.5" />
<param name="Example8" value="8. You Try!;x^2;0;1;0;2;false;true;-5,5,-5,5" />

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 that defines f(x).
3. The expression that defines g(x).
4. The x location of the moveable slice rectangle (the center of the rectangle).
5. The value for "a", the lower limit.
6. The value for "b", the upper limit.
7. The xmin, xmax, ymin and ymax values for the graph region, separated by commas.

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