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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 , approximating the 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 .

Instructions:
Screen Shot
1) Start the program. The screen depicted at right will appear. Press 'Enter'.
2) The next screen contains instructions, as shown at right.
3) Specify the outer integral,...
4) ...the middle integral,...
5) ...and the inner integral.
6) Enter the equation at the prompt.
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.
8) Repeat the process for the middle integral...
9) ... and the inner integral.
10) After a delay (the length of which depends on the number of subdivisions calculated), the result is displayed.
11) Press '2' at this point to quit, and the program exits. Pressing '1' results in the next screen being presented.
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.

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