Texas Instruments TI-83 Manual page 28

Program TRAP
Output: Trapezoidal
b
f (x) dx.
a
Input: f (x) as Y , A as a, B as b, N as n
1
:Disp "A"
:Input A
:Disp "B"
:Input B
:Disp "N"
:Input N
:0→S
:(B-A)/N→H
:A → X
:Y → U
1
:B → X
:Y → V
1
:A + H → X
:Lbl 1
:S+Y →S
1
:X + H → X
:If X < B .5H
:Goto 1
:(.5U + S + .5V )H → T
:Disp "T ="
:Disp T
:Stop
VOL
Output: The Riemann sums
n
f (x , y )hw where h = (b
i j
i,j=1
with (x , y ) taken first at the lower left-hand corner
i j
of each subrectangle and then at the upper right-hand
corner. The function z = f (x, y) is defined on the rect-
angle D = {(x, y) : A ≤ x ≤ B, C ≤ y ≤ D }. The
program pauses after the first Riemann sum. Press RE-
TURN to obtain the second sum.
Input: f (x, y) as Y , A as a, B as b, C as c, D as d, N
1
as n.
:Disp "A ="
:Input A
:Disp "B ="
:Input B
:Disp "C ="
:Input C
:Disp "D ="
:Input D
:Disp "N ="
rule approximation
a)/n, w = (d c)/n
:Input N
:0 → S
to
:(B A)/N → H
:(D C)/N → W
:A + H → X
:C + W → Y
:Lbl 1
:S + Y → S
1
:Y + W → Y
:If Y < D .5 ∗ W
:Goto 1
:C + W → Y
:X + H → X
:If X < B .5 ∗ H
:Goto 1
:S → L
:A → X
:C → Y
:Lbl 2
:Y + L → L
1
:Y + W → Y
:If Y < D .5 ∗ W
:Goto 2
:A + H → X
:C → Y
:Lbl 3
:Y + L → L
1
:X + H → X
:If X < B .5 ∗ H
:Goto 3
:L ∗ H ∗ W → L
:Disp L
:Pause
:S → R
:A + H → X
:D → Y
:Lbl 4
:R + Y → R
1
:X + H → X
:If X < B + .5 ∗ H
:Goto 4
:B → X
:C + W → Y
:Lbl 5
:R + Y → R
1
:Y + W → Y
:If Y < D .5 ∗ W
:Goto 5
:R ∗ H ∗ W → R
:Disp R
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