PUT INTAPP.82p                       
TI82 program to display Riemann sums.  Function, bounds, number of 
variables, type of sum can all be customized.
----begin documentation----            
This program is designed to demonstrate the various ways of doing
a Riemann summ.  It is useful in teaching the concept of the definite
integral.  

The program asks the user to supply a function which is then stored in Y1.
The user is also asked for upper and lower bounds, number of subintervals,
and the method of sum desired.  The program computes a convenient window for 
graphing, then draws the function along with the approximating rectangles
and computes the sum.  It should be noted that the program uses the min and 
max functions to set the upper and lower bounds for the y range.  Since
these functions use a seed to find a local min and max, functions with
a local min or max in the designated x range may continue off the screen.

When running the program, the user is reminded that on the TI-82, 
inputing a function through a program requires that the function 
start with a double quote mark.

The function is stored in Y1.
The program uses the variables: 
U, L, and N are the upper and lower limits of X, and the number of 
subintervals respectively.
H and S are the width of a subinterval and the Riemann sum.
M is the midpoint of a subinterval.
I and Z are counters and dummy variables.

The program puts the calculator in function mode and turns off the
graphing of variables other than Y1.

This program is joint work of Paul Patterson and Mike May from
the Department of Mathematics and Computer Science at Saint Louis 
University.  Send comments to:
maymk@slu.edu
----end documentation----              
 ----begin ASCII----                         
\START82\
\COMMENT=Program file dated 01/24/96, 16:54
\NAME=INTAPPX
\FILE=INTAPPX.82p
Func
FnOff 
Disp "ENTER FUNCTION"
Disp "DON'T FORGET THE"
Disp "QUOTES BEFORE"
Disp "THE FUNCTION"
Input \Y1\
Disp "ENTER LOWER LIMIT"
Prompt L
Disp "ENTER UPPER LIMIT"
Prompt U
L\->\Xmin
U\->\Xmax
min(0,\Y1\(fMin(\Y1\,X,L,U)))\->\Ymin
max(0,\Y1\(fMax(\Y1\,X,L,U)))\->\Ymax
Ymax-Ymin\->\H
(H/54)*6+Ymax\->\Ymax
\(-)\(H/54)*2+Ymin\->\Ymin
max(1,iPart ((U-L)/10))\->\Xscl
max(1,iPart (H/10))\->\Yscl
Disp "X TIC, Y TIC",Xscl,Yscl
Disp "Y MIN, Y MAX",Ymin,Ymax
Disp "HIT ENTER"
Pause 
1\->\Z
Repeat Z=0
ClrDraw
Lbl X
Disp "NUMBER OF SUB"
Disp "INTERVALS"
Prompt N
If N\>=\1
Goto Y
Disp "NEED \>=\ 1"
Goto X
Lbl Y
Menu("TYPE APPROX","MINIMUM",A,"MAXIMUM",B,"LEFT SUM",C,"RIGHT SUM",D,"\#\
MIDPOINT",F,"TRAPZOID",G)
Lbl A
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
fMin(\Y1\,X,L+(I*\@\),L+(I+1)*\@\)\->\M
S+\@\*\Y1\(M)\->\S
Line(L+I*\@\,0,L+I*\@\,\Y1\(M))
Line(L+I*\@\,\Y1\(M),L+(I+1)*\@\,\Y1\(M))
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,\Y1\(M))
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl B
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
fMax(\Y1\,X,L+(I*\@\),L+(I+1)*\@\)\->\M
S+\@\*\Y1\(M)\->\S
Line(L+I*\@\,0,L+I*\@\,\Y1\(M))
Line(L+I*\@\,\Y1\(M),L+(I+1)*\@\,\Y1\(M))
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,\Y1\(M))
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl C
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
\Y1\(L+I*\@\)\->\M
S+\@\*M\->\S
Line(L+I*\@\,0,L+I*\@\,M)
Line(L+I*\@\,M,L+(I+1)*\@\,M)
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,M)
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl D
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
\Y1\(L+(I+1)*\@\)\->\M
S+\@\*M\->\S
Line(L+I*\@\,0,L+I*\@\,M)
Line(L+I*\@\,M,L+(I+1)*\@\,M)
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,M)
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl F
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
\Y1\(L+(I+.5)*\@\)\->\M
S+\@\*M\->\S
Line(L+I*\@\,0,L+I*\@\,M)
Line(L+I*\@\,M,L+(I+1)*\@\,M)
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,M)
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl G
(U-L)/N\->\\@\
0\->\S
For(I,0,N-1,1)
.5(\Y1\(L+I*\@\)+\Y1\(L+(I+1)*\@\))\->\M
S+\@\*M\->\S
Line(L+I*\@\,0,L+I*\@\,\Y1\(L+I*\@\))
Line(L+I*\@\,\Y1\(L+I*\@\),L+(I+1)*\@\,\Y1\(L+(I+1)*\@\))
Line(L+(I+1)*\@\,0,L+(I+1)*\@\,\Y1\(L+(I+1)*\@\))
End
Text(0,2,"AREA=",S)
Pause 
Goto E
Lbl E
Disp "ANOTHER APPROX?"
Disp "0 FOR NO,1 YES"
Prompt Z
End
\STOP82\
----end ASCII----
----begin UUE----
begin 664 INTAPPX.82p
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end 
----end UUE----                        
    eof  (end of file)