*General: *
To type an upper case letter, press ALPHA key, followed by the letter.
To begin entering the program, press the PGRM key, and select NEW from
the menu. The calculator will go into ALPHA mode and prompt you to
enter the name. Type in (for example) LEFTSUM and press ENTER.
The program now displays a colon : which * must appear at the
beginning of each command*.

To enter the program commands (all the words in the program that
start with a Capital Letter), press PRGM key, then select one of
the two menus:

- CTL (Control commands)
- I/O (Imput-output commands).

Commands: Remarks and keying instructions::Prompt A,B,N Program asks for A, B and N. Prompt is 2 on the I/O menu. :A->X For ->, press STO key. For X, Press the [X,T,theta] key. This command sets the variable X equal to the input A. :0->S 0 is zero! (S will be the running total of the sum) :1->I I counts the number of steps taken :(B-A)/N->H - is the key to the right of the 6 key. For /, press the division key, which is under the ^ key. :Lbl P This spot in the program is labelled P. Lbl is 9 on the CTL menu; access this menu with the PRGM key. :S+Y1*H->S For Y1 (the value of the function you are summing, at the current X) press Y-VARS (2nd VARS), select Function, select Y1, ENTER. For *, press the multiplication key, which is to the right of the 9 key. :X+H->X Update X. :IS>(I,N) IS>( is on the CTL menu. The comma is the key below SIN. This command ("Increment and Skip on test") adds 1 to I. If the new I-value is greater than N, the next instruction in the program is skipped. (So if I+1>N, i.e. I is greater than or equal to N, program skips to Disp "LSUM",S; other-wise it recycles to the Lbl P command.) :Goto P :Disp "LSUM",S " is ALPHA +

*Running the program:*
First you have to type in the expression for the function you want to
sum. Press the Y= key (under screen) and enter your function as Y1.
Use the [X,T,theta] key for your variable. As a test, put in x-cubed,
i.e. [X,T,theta], then ^, then 3, then ENTER. Then press QUIT.
Now to run the sum, press PRGM, select EXEC, and select LEFTSUM (It is selected
automatically if it is the only program you have.) The screen will display
a prompt pgrmLEFTSUM. press ENTER. Enter the A, B, N you want at the question
mark (?) prompts.

*Some trouble shooting:*
When typing in the program, be sure to use the STO key as above , and
**not** the equality (=) key!!

*Check:* For Y1=f(x)=x^3, lower limit 1, upper limit 3, and
N = 100, left-hand sum should be 19.7408.

*Exercise:* Rewrite this program to give right-hand sums.

**RIGHT HAND SUMS AND THE TRAPEZOID RULE**

Add these instructions to the end of the program:

:A->X For ->,X,Y1,*,Disp," follow the keying :S-Y1*H->R instructions above. :B->X :R+Y1*H->R :Disp "RSUM",R :(S+R)/2->T :Disp "TRAP",T

*Check:* For Y1=f(X)=sin X, lower limit 0, upper limit pi/2, and
N = 10, LSUM = .91940317, RSUM = 1.076482803, TRAP = .9979429864.

Math Dept SUNY Stony Brook

tony@math.sunysb.edu

September 8 1997