This is a program for the TI-85 which will approximate a definite integral using left, right, and midpoint Riemann sums, the trapezoid method, and Simpson's rule. For partition length n, these numerical approximations are respectively denoted by L_n, R_n, M_n, T_n, and S_n.

To use the program, one must input a formula for the integrand F(x), values for the lower and upper limits of integration a and b, and the desired partition length n. The output will be the numerical approximations L_n, R_n, M_n, T_n and S_n. To exit the program use the ON key (at the lower left corner of the TI-85 keyboard).

:Disp" "
:Disp"Approximating a" 
:Disp"definite integral"
:Disp" "
:InpSt "F(x)= ",FCN
:St>Eq(FCN,F)
:Input "a= ",A
:Input "b= ",B
:ClLCD
:
:Lbl NEWn
:Input "n= ",N
:(B-A)/N->H
:0->L
:0->R
:0->M
:0->T
:0->S
:0->YP
:evalF(F,x,A)->Y
:1->JS
:
:For(J,1,N,1)
: YP->YPP
: Y->YP
: evalF(F,x,A+J*H)->Y
: evalF(F,x,A+(J-.5)*H)->YM
:
: L+YP*H->L
: R+Y*H->R
: M+YM*H->M
: T+(YP+Y)*H/2->T
: L+YP*H->L
: If JS==0
:  Then
:   S+(YPP+4*YP+Y)*H/3->S
:   1->JS
:  Else
:   0->JS
: End
:End
:
:Disp "Ln,Rn,Mn,Tn,Sn= ",L,R,S,M,T,S
:Pause
:Goto NEWn

To understand how this code works, note that L, R, M, T, and S respectively denote L_n, R_n, M_n, T_n, and S_n. Also J denotes the variable of summation; H is the length of the subintervals in the partition; Y and YP are the functional values of the right and left endpoints of the Jth subinterval respectively ; and YPP is the functional value of the left endpoint of the (J-1)st subinterval.

[In the code as typed above, the symbols "St>Eq(" and "evalF(" can be found on the TI-85's CATALOG menu. The symbol "->" is obtained using the "STO>" key which is the second key from the lefthand bottom of the calculator. Many of the other command words can be found on the I/O and CTL menus which are available when editing programs. The greater than and less than symbols may be found on the TEST menu.]

This document was created on November 18, 1998 and revised on
Nov. 24.