Integrate  -  Mathematical function integrator

by Andrew Benson

Integrate is a small application which performs numerical integration of mathematical functions to any specified degree of accuracy.

For non-mathematicians this means that if you enter a suitable equation into Integrate then it will calculate the area under a graph of that equation. As an example, the Draw file HelpGraph (located inside the !Integrate application directory) contains a plot of the graph y=(2*x)+1. The shaded area on the graph is the area which would be calculated by Integrate if you entered this equation into it.

Integration of equations can of course be done mathematically with pencil and paper. However, some equations are very difficult to integrate and so a numerical method is used to estimate the result. This is what Integrate does. It can also be used to check the results calculated mathematically.

Using the Application
Integrate is very simple to use. The application is run in the usual way by double-clicking on its icon in a directory viewer. An icon is installed on the icon bar. Clicking Menu over this icon will display a menu containing the usual Info and Quit entries.

Clicking Select on the icon bar icon will open a small window into which you can enter the equation to be integrated. To do this, simply type the function into the writable icon labelled f(x)=. The equation can include any of the normal mathematical functions that the computer understands (e.g. +-/*, SIN, COS, TAN, EXP, LOG etc.). Make sure that you enter the variable as 'x' not 'X'.

The function must be integrated over a range of x values. Enter the minimum and maximum values of x in the two icons labelled Min. x and Max. x respectively. Finally you must enter the size of increment used in the calculation. The smaller this increment the more accurate the answer will be, but the longer the calculation will take. As an initial step try entering a value which is about one tenth the size of the range of x values (i.e. if the x range was from 0 to 3 then try 0.3 for a start). If you discover that you want a more accurate result and don't mind waiting a little longer, then decrease the increment and try again.

Once all of this has been entered simply click on the Integrate icon. The hourglass will be displayed together with the percentage figure which indicates how far the integration has progressed. Once the integration is complete the result will be displayed at the bottom of the window.

Copyright  RISC User 1995
