Defint V100
By Chris Nojima

Purpose of program:
To help calculus students with their integrals using the Riemann (Left
Right and Mid) sum, simpsons rule, trapezoidal rule, and the calcs built
in function. Not only does this program allow you to solve the integral
by those methods, there is a function to solve it using all the above 
methods side by side, so you can see the differences and relationships
between them.  Aside from finding integrals, this program can also graph 
the function and shade in the region of the integral (great for overhead
use).  And lastly this program has a function to find one bound when given
the other bound and the integral (more info below).

Instructions:
This program is menu driven and is pretty easy to figure out.

It first prompts you for your equation f(x)
After you input the function you have to give it your lower and upper bounds
for the integral.
Lastly you are asked for how many subintervals you wish to use.

Thats all the inputting you need to do.  Next there is a menu

Choose which method you with to use. (if you choose to use Riemann sums, 
there is a second menu which asks for Left Mid or Right)

For other options press F5 (More>)

Choose "ALL" for side by side comparison of integral methods
Choose "Shade" to draw the graph (it will prompt for you graph window settings)

The only function that needs explaining is "Solve". It basically works like this. 

This function is kind-of a solver for integrals. Given one limit (lower or upper, 
which you gave in the beginning), and the integral, it will find the other limit.
e.g.

f(x)=1
lower=0
upper=10 (this doesn't really matter)
subintervals=1 (this doesn't matter either)

goto the solve function

we know our lower limit, so we choose lower in the menu
our integral is 0, so we make
integral value=10

we have to give it a guess value, since we could run into problems with multiple
solutions to the integral (e.g. f(x)=sin x when lower limit is 0, and integral is 2.4, the 
upper limit could be anywhere)
so, guess=8

then it tells us that the lower=0 and the upper=10
that's basically it(whee!)

If you have any version of defint by me before this version DESTROY IT
This program was made because my old calc teacher had several different programs
(one did riemann, one did simpsons, etc). So i decided to put it all together in
one program. After i put it together, i released it, not knowing that the algorithms
used to calculate the methods were slow/wrong. I am pretty sure these are right
if they are wrong please email me at wnc@wco.com . 

Feel free to edit this program if you want to, if you happen to make it better
mail me a copy so i can learn ;)

Chris Nojima 12-3-96