Multiple Integration with MPP, the Mathematics Plotting Program

Double Integration:

Step 1. Start the MPP (2D version)

Step 2. Choose Item 9 in the list, then press "Enter"

Step 3. Read the information on the blue screen, and then press "Enter"

Step 4. Choose "Rectangular" or "Polar" in Section F1 by typing 1 or 2

Step 5. Choose the order of integration in Section F2, depending on the problem you are trying to solve

Step 6. Fill in the blanks; note the following:
-- use * for multiplication, and parentheses, if there is a confusion in reading information; for instance, the expression "xsiny" may return an error, so type x*sin(y)
-- type "pi" for the corresponding greek letter;
-- when in polar coordinates, press "Ctrl-T" to type the greek letter for theta

Step 7. When finished entering numbers and functions, pressing "F9" should show a graph of the region of integration shaded out, together with a numerical estimate of the integral on the left of the screen. Press "H" for a menu from which you may choose to do various things; in particular, you may print your results.

Triple Integration:

Follow the same 7 steps as in double integration, with the following changes:

In Step 2, choose Item A;
In Step 4, choose between "Rectangular", "Cylindrical" or "Spherical"
In Step 7, only the numerical estimate is shown. To graph the region of integration, use either the MPP3D graphing program or the DPGraph 2000 (the latter provides more options and capabilities for 3D graphing).

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