Bright Ideas Software - Calculus Visualization Tools Click here to return to the BIS Home Page.

TI-83 Programs

  Skip Navigation LinksHome --> Math Tools --> TI-83 Programs --> 3D Riemann Sum Search:
  Skip Navigation Links
Math ToolsExpand Math Tools
DevelopersExpand Developers
About BISExpand About BIS
Skip Navigation Links

Skip Navigation Links

This program calculates a Riemann sum for a function having three independent variables, taking the form R=F(x,y,z); that is, it calculates the sum 3D Riemann Sum, approximating the integral Triple integral. As with the 2D Riemann program, this allows the use of expressions in the inner two integrals, allowing integration of non-rectangular volumes; it is necessary, however, to specify the order of integration. Values for each sub-region are calculated at the center of the sub-region.

Note: This program uses the calculator's 'Y0', 'Y9', 'Y8', 'Y7' and 'Y6' graphing functions in it's calculations, and will overwrite any equations previously stored there.

Using the Program:

The following example demonstrates the use of the program to give an approximate solution to the triple integral Sample 3D sum.

Screen Shot
1) Start the program. The screen depicted at right will appear. Press 'Enter'. Rmn3D Screenshot 1
2) The next screen contains instructions, as shown at right. Rmn3D Screenshot 2
3) Specify the outer integral,... Rmn3D Screenshot 3
4) ...the middle integral,... Rmn3D Screenshot 4
5) ...and the inner integral. Rmn3D Screenshot 5
6) Enter the equation at the prompt. Rmn3D Screenshot 6
7) Specify the limit information and subdivisions for the outer integral. (Use a bit of caution here - selecting too high a subdivision count will result in an unacceptably long delay. Just how big a count is too big varies with calculator model and user mood.) Press 'Enter' after entering each value. Rmn3D Screenshot 7
8) Repeat the process for the middle integral... Rmn3D Screenshot 8
9) ... and the inner integral. Rmn3D Screenshot 9
10) After a delay (the length of which depends on the number of subdivisions calculated), the result is displayed. Rmn3D Screenshot 10
11) Press '2' at this point to quit, and the program exits. Pressing '1' results in the next screen being presented. Rmn3D Screenshot 11
12) Press '1' here and you can enter a new function; press '2' and that step is skipped, and you are prompted for new limit and subdivision values. Rmn3D Screenshot 12

Back To Top

Copyright© 2001-2017 by Bright Ideas Software®. All rights reserved.