### Program for Riemann Sums on TI-85 and 86

(Copied from Nicolas Baeth)

#### Program for left and right hand sums:

Disp "LOWER LIMIT"

Input A

Disp "UPPER LIMIT"

Input B

Disp "DIVISIONS"

Input N

A -> x

0 -> S

1 -> I

(B-A)/N -> H

Lbl P

S+y1*H -> S

x+H -> x

IS>(I,N)

Goto P

Disp "LEFT SUM"

Disp S

S+y1*H -> S

Disp "RIGHT SUM"

Disp S

(Make sure that you enter the function into the value for y1 before you
run the program or else it will not know what function you wish to
estimate for.)

#### Program for left/right hand sums plus simpsons/midpoint/trapezoid
estimates:

Disp "LOWER LIMIT"

Input A

Disp "UPPER LIMIT"

Input B

Disp "DIVISIONS"

Input N

(B-A)/N -> H

A -> x

0 -> L

0 -> M

1 -> I

Lbl P

L+H*y1 -> L

x+0.5H -> x

M+H*y1 -> M

x+0.5H -> x

IS>(I,N)

Goto P

Disp "LEFT/RIGHT"

Disp L

L+H*y1 -> R

A -> x

R-H*y1 -> R

Disp R

(L+R)/2 -> T

Disp "TRAP/MID/SIMP"

Disp T

Disp M

(2*M+T)/3 -> S

Disp S

(Pause)

(This last line is optional, but without it I find that part of the output
leaves the screen before it can be read.)