Program: Integral
By: Ben Axelrod

   This program will show you what the graph of the integral of a 
function looks like.  It will also numerically evaluate it using the 
trapezoid method.  

Entering your function and range:
   First type in the function that you want to integrate at the prompt.  
(X is the independent variable)  Then enter the range that you want to 
evaluate or graph.  Remember, if your function is 1/x and you want to 
evaluate it from 0 to some number, you have to type 0.001 or something 
similar instead of 0.  You will get a divide by 0 error if you try to use 
0.  

Entering number of points:
   Now enter the number of pieces you want the program to divide the 
range into, to sum the areas.  This number depends on a couple of different 
factors.  If you just want to see the graph of the function, then you will 
want a smaller number of points.  Probably around 50 or 100 should be good. 
 However if you really want an accurate numerical evaluation, then you 
should go with 500 or more points.  Keep in mind that the more points you 
choose, the more accurate your answer will be, and the longer it will take 
to calculate.  Depending on the function, 500 points could take a minute or 
two to calculate.  Lastly, the range you choose also should determine how 
many points you want.  If you have a range from 1 to 100, obviously you 
will need more points than a range of 0 to 1.  

Important:
   The graph of the function uses lists to store data points.  These 
lists cannot exceed 999 entries.  So dont enter more than 999 points unless 
you edit the program yourself and take out the graphing ability.  If you want 
a very accurate numerical evaluation, a better method would be to use the 
fnInt( function in the math menu.  It is much more accurate than my program 
not to mention faster.  

Next:
   Now the program will display THINKING  It is thinking, be patient. 
The numbers you see in the upper left corner of the screen, is the percent 
done.  That way you can track its progress.  Finally, when it is done thinking,
you can see the graph.  At the bottom of the screen is the original function 
and the numerically evaluated integral.  

About the graphing:  
   Due to the way the program works, the first data point of the graph 
will always be on the X axis.  This program will only show you the shape of 
the integral, not the exact function.  Remember, there will be an arbitrary 
constant added anyways.  If the locations of the axes are bothersome, you 
can turn them off and the graphs look much nicer.  Note, the numerical 
evaluation is not affected by this placement of the graph.  They are still 
accurate.  

   The other program included is a fix program.  Integral uses up a lot of 
memory in lists and strings.  IntFix clears this for you.


Questions or comments?  Email me at:  bmaxelro@syr.edu

