## Substitution Applet

Substitution is used to illustrate integration via substitution. It enables input of the outer and inner functions, then graphs the integrand that results from taking the derivative of their composition. It also shows a graph of the derivative of the outer function, with the limits of integration converted via the inner function. The result is that the areas under the two curves are the same.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.Substitution" codebase="../../assets"

archive="webcompmath.jar,calculus.jar" height="400" width="640">

<param name="UseLoadButton" value="no" />

<param name="Example1" value="1. Substitution;e^u;x^2;0;2;-1,6,-5,20" />

<param name="Example2" value="2. More Substitution;e^u;sin(x);0;2;-5,5,-5,5" />

</applet>

This applet takes the following parameters:

Param NameTypeDefaultDescriptionExample1, ...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(u), the outer function.

3. The expression for u = g(x), the inner function.

4. The initial value for a, the lower limit.

5. The initial value for b, the upper limit.

6. The values for xmin, xmax, ymin, and ymax, as a comma-separated list.