Commands: Remarks and keying instructions: :Prompt A,B,N Program will ask you to key in A (initial x-value), B (final x-value) and N (the number of equal subdivisions). To get Prompt, press PRGM, F3, F2. :A->x For ->, press STO key. For x, Press x-VAR key. :0->S This 0 is zero! These 3 commands initialize x, S, and the counter I. :1->I :(B-A)/N->H Calculate subdivision length. - 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. To get Lbl, press F4 (CTL menu), MORE (to scroll the CTL menu) and F4. :S+y1*H->S Add H times the current value of y1 (the function being summed) to S. For y (lower case!) use 2nd ALPHA; for *, press the multiplication key, which is to the right of the 9 key. :x+H->x Update x. :IS>(I,N) IS> increments I by 1 and tests if the new I is larger than N. If so, the program skips the next step (and displays the sum); Otherwise it cycles back to P. For IS>(, press F4 key (chooses CTL menu), then twice the MORE key, then F1. Note: the comma is the key to the left of the 4 key. :Goto P For Goto, press F4, MORE, F5 :Disp "LSUM",S For Disp, press F3,F3; for " F3,MORE,F5Ending: After pressing the ENTER key for the last command, press the EXIT key.
Running the program:
Press GRAPH key, then F1 key, then key in the expression for the function
you want to sum (e.g. x-VAR, then ^, then 3 for f(x)=x^3). Use x-VAR for
your variable. Then EXIT, EXIT.
Now press PRGM, then F1, then the F-key under the word LSUM in the screen, then the ENTER key. Enter numbers at the question mark (?) prompts.
Check: for y1=f(x)=x^3, lower limit 1, upper limit 3, and 100 subdivisions, left-hand sum should be 19.7408.
Exercise: Modify this program to do right-hand sums.
RIGHT HAND SUMS AND THE TRAPEZOID RULE
Add these instructions to the end of the program:
:A->x For ->,x,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",TCheck: For y1=f(X)=sin X, lower limit 0, upper limit pi/2, and N = 10, LSUM = .919403170015, RSUM = 1.07648280269, TRAP = .997942986354.