PROGRAMS FOR NUMERICAL INTEGRATION:

Left and right hand Riemann Sums, Trapezoid Rule, Midpoint Rule, and Simpson's Rule. (L,R,T,M,S)

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Remember to enter the programming steps from the catalog or in some way that recognizes them as programming commands. In other words, don't just enter them in as alphabetical characters. It has been reported that the TI-81 program works for the TI-83, but it appears to be still running even while paused. Just hit "ON" and quit to stop everything.

I've been informed that there are Internet sites that have programs for doing these sums. I will post them when I have the addresses.

TI-81

(this can be adapted to many other programable calculators)

To use, simply enter Y1 = f(x). To change limits on the integral enter "0" when prompted for N.

Prgm1:INTEGRAL
:Lbl 3
:Disp "LOWER"
:Input A
:Disp "UPPER"
:Input B
:Lbl 2
:Disp "N"
:Input N
:If N£ 0
:Goto 3
:(B-A)/2N® H
:0® L
:0® M
:1® J
:A® X
:Lbl 1
:L+Y1
®L
:X+H® X
:M+Y1
®M
:X+H® X
:IS>(J,N)
:Goto 1
:Disp"L/R/T"
:2HL® L
:Disp L
:L+2HY1
®T
:A® X
:T-2HY1
® T
:Disp T
:(L+T)/2® T
:Disp T
:Disp "MID/SIM"
:2HM® M
:Disp M
:(2M+T)/3® S
:Disp S
:Pause
:Goto 2

 

TI-85

(you can use different labels for things like cc, bb, aa as long as you're consistent)

To use, simply enter y1 = f(x). To change limits on the integral enter "0" when prompted for N.

Prgm:INTEGRAL
:Lbl cc
:Disp "Lower Limit"
:Input A
:Disp "Upper Limit"
:Input B
:Lbl bb
:Disp "Divisions"
:Input N
:If N£ 0
:Goto cc
:(B-A)/2N® H
:0® L
:0® M
:1® J
:A® x
:Lbl aa
:L+y1® L
:x+H® x
:M+y1® M
:x+H® x
:IS>(J,N)
:Goto aa
:Disp"Left/Right/Trap"
:2H*L® L
:Disp L
:L+2H*y1® T
:A® x
:T-2H*y1® R
:Disp R
:(L+R)/2® T
:Disp T
:Disp "Midpoint/Simpson"
:2H*M® M
:Disp M
:(2M+T)/3® S
:Disp S
:Pause
:Goto bb