## Integration Applet

Integration is used to explore indefinite integrals. It shows the graph of an integrand and its antiderivative. The applet supports two ways of looking at indefinite integrals. The first way shows a tangent line on the antiderivative curve and the corresponding point on the integrand, showing that the integrand is the derivative of the antiderivative. The second method uses the idea of an accumulation function. This shows area under the integrand colored in, and shows the corresponding point on the antiderivative which represents this area. A c input box and slider is provided to show the family of antiderivatives created by adding a constant.

The applet tag that creates the applet is as follows:

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

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

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

<param name="Example1" value="1. Zero;0;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example2" value="2. Constant;2;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example3" value="3. Line;x;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example4" value="4. Parabola;x^2;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example5" value="5. Cubic;x^3;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example6" value="6. Hyperbola;1/x;0;0;-4,4,-4,4;0;(x<0?numInt(t,1,x,f(t),100) + c:numInt(t,-1,x,f(t),100) + c);1" />

<param name="Example7" value="7. Exponential;e^x;0;0;-4,4,-4,4;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example8" value="8. Cosine;cos(x);0;0;-6.28,6.28,-2,2;1;numInt(t,0,x,f(t),100) + c;0" />

<param name="Example9" value="9. Sine;sin(x);0;0;-6.28,6.28,-2,2;1;numInt(t,0,x,f(t),100) + c;0" />

</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 the integrand function f(x).

3. The value for the x input and slider.

4. The value for the c input and slider.

5. The xmin, xmax, ymin and ymax values for both graphs, separated by commas.

6. The inital value of the type choice box. Use "0" for slope and "1" for area.

7. The definition of the antiderivative to be graphed. This can be as simple as the actual antiderivative function, but then if the user edits f(x), the antiderivative graph won't change. It is better to use something likenumInt(t,0,x,f(t),100) + cwhich computes the antiderivative numerically, and adjusts for c. For some special cases, like the hyperbola example shown above, you may need a more complicated antiderivative to handle a vertical asymptote or other such problem.

8. The lower limit for the displayed area colored in under the integrand. Normally this is 0, but for some special cases you may need a different value.