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HP 48g Series Calculators - Riemann Sum Approximations

Description
The following programs can be used on the HP 48g series calculator. Each program is a particular implementation of the Riemann Sum approximation of a definite integral of a continuous function, (see Figure 1).
Figure : Riemann Sum approximation
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key
Description
Text Representation
Right shift key
RS
Left-shift key
LS
Move cursor left
cursor-left
Move cursor right
cursor-right
Move cursor up
cursor-up
Move cursor down
cursor-down
Backspace/clear
backspace
Program entry
  1. To store the following programs in the calculator, it is recommended to create a sub-directory called 'RIEM':
    1. Press RS, then MEMORY
    2. Press NEW
    3. Press cursor-down and enter a name into the NAME field.
    4. Highlight the _DIRECTORY check field, and press CHK (or +/-).
    5. Press OK
  2. Change to the 'RIEM' directory and type in the first program using the program delimiters, [<< >>]. All characters must be entered exactly as shown in the example. Upper case must be upper case and spaces must be included; use the RS, then CHARS menu for characters not located on the keyboard. Then, press ENTER to put the program on the stack. (See the User's Guide for more on programming the HP 48.)
  3. To store the program; press ['], ALPHA, ALPHA and type the program name (e.g. L, R, I, E, M), then ALPHA, STO
  4. Repeat steps 1, 2, and 3 for the other two programs.
      note:
    To enter the WHERE command, press the following keys: LS+SYMBOLIC, then NXT
Program 1 - 'LRIEM'
Left Riemann Sum:
Program 2 - 'MRIEM'
Middle Riemann Sum:
Program #3 - 'RRIEM'
Right Riemann Sum:
Example of finding the Riemann Sum
Find the left-hand, middle, and right-hand sums of the function f(x)= 1/x with 50 subdivisions where 1 is the lower limit and 2 is the upper limit (see Figure 2).
Figure : Riemann Sum example formula
  1. Store the function in the variable EXPR
    1. Press ['], 1, ÷ , ALPHA, X, then ENTER
    2. Press ['], ALPHA, ALPHA, E, X, P, R, ALPHA, then STO
  2. Use the following keystrokes for each program.
Figure : Example program keystrokes
  note:
Use the following program for a simple data entry form.
Optional INFORM window
This program provides a data entry form for Riemann sum programs. Data may be entered once for any combination of the three previous programs. It also remembers the last expression used and defaults to 'Y' for all three Riemann sum programs. Refer to the instructions for keying in programs above. Store the program in 'RSUMS' in the 'RIEM' directory.
Optional program - RSUMS
Press RSUMS in the VAR menu and key in the previous example:
Figure : Riemann Sums screen
The answers from the previous example should look like this:
Figure : Example answers

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