Riemann Sums Program code for the TI-81 graphing calculator
Select PRGM to get the program menu, move to EDIT to enter a program.
When you select a program number, you must first give it a name (for example, 'RSUMS')
to the right of the program number.
Disp "LOWER LIMIT"
Input A
Disp "UPPER LIMIT"
Input B
Disp "DIVNS"
Input N
A --> X
0 --> S
1 --> I
(B - A)/N --> H
Lbl P
S + H*Y_1 --> S
X + H --> X
IS > (I,N)
Goto P
Disp "LEFT SUM"
Disp S
S+H*Y_1 --> S
A --> X
S - H*Y_1 --> S
Disp "RIGHT SUM"
Disp S
Comments on the program listing
- Take care to distinguish between the character 1 (one) and
the character l (lower case "ell"), and between 0 (zero) and O (upper case "oh").
- The symbol --> is an attempt to reproduce the right-pointing arrow.
This arrow is produced by hitting the STO key.
- Y_1 is intended to represent Y with the subscript 1. Y_1 is accessed via Y-VARS, i.e.,
2nd VARS. (Do not use Y followed by 1, which is simply Y multiplied by 1.
- Disp and Input are accessed via PRGM, I/O,
pressed while editing a program.
- The quote mark " is on the + key when you have pressed the ALPHA key.
- Lbl, IS>, and Goto are accessed via PRGM, CTL.
Running the program
- This program calculates left and right Riemann sums.
- Before running the program you need to use the GRAPH key,
to specify the formula for the function f as Y_1, with X as the independent variable.
- The lower limit of integration must be less than the upper limit.
- As a test of the program, evaluate the definite integral of x^3 (x cubed) from A=1 to B=3 using
N=100 subdivisions. The left and right Riemann sums should be 19.7408 and 20.2608, respectively.
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October 23, 1998