## LEFT-HAND SUM PROGRAM

**WITH EXTENSION TO RIGHT-HAND SUMS AND THE TRAPEZOID RULE**
### SHARP EL-9300C or EL-9200

*General:*
To enter the program commands, press the programming key (middle upper key),
then C key (which selects the NEW program option), then ENTER, then 1 (to
select real mode), then the program name. The calculator will be in
A-LOCK mode. Hit ALPHA at the end of the name, and then ENTER. After typing
each command, press the ENTER key.
*Commands: Remarks and keying instructions*
h=(-a + b)/n Use the minus sign below 3 to enter "minus a"
The Sharp automatically prompts for
undefined variables. Here a is the lower
limit, b is the upper limit, and n is the
number of subdivisions
For /, press the division key, under the
the ) key.
s=0 These two commands initialize s (the
i=0 running total for the sum) and the counter i.
Label 1 This spot in the program is labelled 1.
For Label, press 2ndF key followed by COMMAND
key, then B key for the BRNCH (branching
instructions) menu, then 1 key.
x=a+i*h Calculate i-th x-coordinate.
f=x^3 This line defines the function to be
summed. *To change functions, edit this line.*
s=s+f*h Add the next increment to the sum. For *,
press the multiplication key, under the ( key.
i=i+1 Add 1 to the counter.
If i< n Goto 1 For If and Goto get to BRNCH menu as
before, then press 3 key for If and 2 key
for Goto. For < press 2ndF key followed
by COMMAND key, then C key for INEQ menu,
then 2 key. If i is equal to n, (the
sum is complete and) the program goes on to
the next command.
Print s The calculator will display s=(value).
End (optional) For End, goto the PROG menu as
before, then press 6 key.

*Ending:*
After pressing the ENTER key for the last command (End), press the QUIT
key.
*Running the program:*
Remeber to re-edit when you switch functions.
In the program menu (upper middle key) choose A (for RUN menu),
then right arrow then down arrow to LSUM, then ENTER.
Enter numbers at the question mark (a=? etc.) prompts.

*Check:* for f = x^3, lower limit 1, upper limit 3, and 100
subdivisions, the left-hand sum should be 19.7408.

**RIGHT-HAND SUMS AND THE TRAPEZOID RULE **

The program should be modified as follows: (Additions appear in
**boldface**; the command f= .. is moved to the subroutine 2,
the command Print s is deleted. Note that < changes to < =!).

**Goto 0** Start the program where it started before.
**Label 2** These 3 commands form a ``subroutine,'' a
**f=sin x** subprogram that can be accessed from anywhere
**Return** in the program and returns to the accessing
**Label 0** point.
h=(-a + b)/n
s=0
i=0
Label 1
x=a+i*h
**Gosub 2**
s=s+f*h
i=i+1
If i<**=**n Goto 1 Note the change from < to < =. The sum
**l=s-f*h** s uses both the initial and the final values.
**Print l** Subtracting the final contribution (sb) gives
**x=a** the left-sum l; subtracting the initial
**Gosub 2** contribution gives the right-sum r.
**r=s-f*h**
**Print r
t=(l+r)/2
Print t**
End

*Check:* For f=sin x, lower limit 0, upper limit pi/2, and n = 10,
you should get left-sum l = .91940317, right-sum r = 1.076482803,
and trapezoid approximation t = 0.997942986.

*
Anthony Phillips*

Math Dept SUNY Stony Brook

tony@math.sunysb.edu

September 8 1997