Graphing Calculator Programs for Numerical Integration

Finite Mathematics Applied to the Real World

Calculus Applied to the Real World

Finite Mathematics & Calculus Applied to the Real World

Below are listed two programs that you can use to calculate approximations to the definite integral. The first of these gives the left- and right-hand Riemann sums and trapezoidal sum of a given function, while the second gives the Simpson's rule approximation. To enter these programs, you should consult the section on programming in your user manual. (There is also a useful table of instructions and functions, together with the keystroke sequences needed to obtain them, at the back of the manual.)

For an on-line utility that does numerical integration, press here.

PROGRAM: SUMS
:Input ("NUMBER OF INTERVALS? ",N)
:Input ("LEFT ENDPOINT? ",A)
:Input ("RIGHT ENDPOINT? ",B)
:(B-A)/ND
:ØR
:ØL
:AX
:For (I,1,N)
:L+Y1L
:A+I*DX
:R+Y1R
:End
:L*DL
:R*DR
:(L+R)/2T
:Disp "LEFT SUM IS ",L
:Disp "RIGHT SUM IS ",R
:Disp "TRAP SUM IS ",T
:Stop

Graphing Calculator Program for Simpson's Rule (TI-82/TI-83)

PROGRAM: SIMP
:Input ("EVEN NUMBER OF SUBDIVISIONS? ",N)
:Input ("LEFT ENDPOINT? ",A)
:Input ("RIGHT ENDPOINT? ",B)
:(B-A)/ND
:ØS
:AX
:For (I,1,N-1,2)
:S+Y1S
:A+I*DX f(xi-1) + 4f(xi) + f(xi+1) )
:S+4*Y1S
:X+DX
:S+Y1S
:End
:S*D/3S
:Disp "SIMPSON SUM IS ",S
:Stop

Using the Programs

To use the above programs, first enter the function f(x) whose sums you wish to compute as Y1 in the "Y=" window. Then run the program. It will first ask for N, which is the number of partitions you wish to use. Enter the number (which must be at least 1) and then press "ENTER". (If you are running SIMP, make sure that the number you enter is even and at least 2.) Next, it will ask for the values of A and B in that order, so you enter them in the same way. Then wait a while (the larger N is, the longer the wait), and the answers will appear.