The Integration options can be changed by selecting the Integration tab of the Settings dialog (Options/Settings menu), or more directly by clicking the Options button on the Integrate Curve dialog box. This dialog box allows you to change the following options:
Method of Integration
You may choose between the following methods of integration:
| Rectangles Above | Region is broken up into rectangles whose upper and lower bounds are strictly above the curve(s) being integrated. |
| Rectangles Below | Region is broken up into rectangles whose upper and lower bounds are strictly below the curve(s) being integrated. |
| Left-hand Sums | Region is broken up into rectangles whose upper and lower bounds are determined by the points where their left-hand sides touch the curve(s). |
| Right-hand Sums | Region is broken up into rectangles whose upper and lower bounds are determined by the points where their right-hand sides touch the curve(s). |
| Trapezoidal Rule | Region is decomposed into trapezoids with the base of the trapezoid on the x axis and the slanted edge of the trapezoid approximating the curve |
| Simpson's Rule | Each segment of the curve is approximated by a quadratic function. Generally more accurate for smooth curves. |
Number of Segments
By default, the program chooses how many segments to use based on the amount of screen space the region covers. The number chosen provides the fastest calculation which is accurate to the precision of the displayed result using Simpson's rule. Alternatively, you can specify the number of segments you wish to use in the approximation in the edit box. This number must be a positive integer, and must be even if you want to use Simpson's Rule.
If you specify the number of segments manually and the individual segments are wide enough (more than 5 pixels wide), Graphmatica will draw in the boundaries of each segment separately for all methods except Simpson's rule. Although the result of the calculation will probably be inaccurate with segments this wide, the graphic makes the way the result was obtained more intuitive.
Input Method
Use the two checkboxes at the bottom of the dialog to choose between the two different ways of specifying which equation(s) to integrate over which region. You can select one or both of them.
Select initial curve/region with mouse After you choose the Integrate menu item, click on a curve at one end of the region and drag out the region to integrate (release the mouse over a second curve to find the area between the curves).
Show Integrate Curve dialog box This is a modeless dialog box which lets you choose one or two equations (to find the area under a curve or the area between two curves) and enter the boundaries of a region to integrate over, then displays the result of the calculation. If the box above is checked as well, this dialog comes up (if not already up) after you make your initial selections with the mouse. If not, it comes up immediately when you select the Integrate menu item. This dialog box stays up until you dismiss it, or until you hide or delete the equation(s) for which the integral shading is displayed.
The integration options you select are saved in GRAPHMAT.INI when you choose Save Setup from the File menu. They are not included in normal equation list files.