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FundamentalTheorem Applet

FundamentalTheorem is used to illustrate the Fundamental Theorem, showing that the value of a definite integral is the difference of the values of the antiderivative evaluated at the two limits of integration. It shows a graph of the antiderivative f(x) with a vertical bar on the y axis, which illustrates the difference between the two values of the antiderivative. It also shows a graph of the derivative f '(x) (i.e., the integrand) and colors in the area under this curve between the limits. The length of the line in the first graph equals the area in the second graph.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.FundamentalTheorem" codebase="../../assets"
archive="webcompmath.jar,calculus.jar" height="480" width="640">
<param name="UseLoadButton" value="no" />
<param name="Example1" value="1. Line;20x;0;8;-0.5,8,-10,160;0;8;0;8" />
<param name="Example2" value="2. Cubic;-1/3*x^3+15/2*x^2+20x;0;8;-0.5,8,-50,500;0;8;0;8" />
<param name="Example3" value="3. Parabola;x^2;1;3;-4,4,-8,16;-4;4;-4;4" />

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 antiderivative 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. The minimum value for the a slider.
7. The maximum value for the a slider.
8. The minimum value for the b slider.
9. The maximum value for the b slider.

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