Simpsons Rule Formula

   Yea so there are a few Simpson's rule programs out there, and the TI-85/6 can do it anyway but I think mine is definetly user friendly and gives you a little more insight.

   Well all the things in this program are used to solve numerical integration. If you don't know what that is then this program is useless to you. Integration by itself is kind of like the reverse of the derivitive. Now if you don't know what that is then you just wasted your time and disk space getting this. Normal integration can be simple like (forgive the crueness) |x^n = (x^n+1)/(n+1) so the integral of x^3 = x^4/4. This is simple and easy to solve. however something like      1
			         -----          e^ ((-x^2)/2)
                            square root (2*pi)

can't be solved simboliclly. So you just have to sub in numbers and find the area under the curve. This is called numerical integration. Left Hand and Right Hand Reinmann sums are crude but can be used to find the area. Using the Trapazoidal is much better, but still off. It's just the Right and Left hand sums averaged. Finding the midpoint areas is even better. Simpsons rule is the best because as far as decimal approximation goes and how many subdivisions you use, it is right on the answer. Simpson's rule takes the Trapzoidal answer adds it to two times the mid number and divides by three.

   My program find all these values and outputs them all out so you can see how they all contribute to the final answer. You can also review your function, and find out what the individual numbers in the sums were. This program only takes up 757 bytes. If you want the smaller program that only takes 398 bytes and is fully functional, but less user friendly:

:ClLCD
:InpST "f(x)=",A
:StEq(A,y1)
:Input "Low Bound: ",B
:Input "High Bound: ",C
:Input "Divisions: ",D
:(C-B)/DI
:I(sum seq(y1,x,B,C-I,I)L
:I(sum seq(y1,x,B+I,C,I)R
:(L+R)/2T
:I(sum seq(y1,x,B+(I/2),C-(I/2),I))M
:(T+(2*M))/3S
:ClLCD
:Outpt(1,12,L)
:Outpt(2,12,R)
:Outpt(3,12,T)
:Outpt(4,12,M)
:Outpt(5,12,S)
:Disp "Left Hand","Right Hand","Trapazoid","Midpoint","Simpsons","    "

   The "" is the store as arrow and the "" is the dark right arrowhead. Darn the limitations of notepad. Yea yea, some super geek is gonna complain that I could have shrunken it to like 200 or something while laughing at how big this is but both do the job in a FEW cases faster then in the math menu in graph mode but generally it takes a minute to get all the sums so just bear with it. Thanks for taking a look at my program.