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This program calculates a variety of Riemann Sums on a function with one independent variable, taking the form Y= F(x); that is to say, it approximates the integral Single variable integral. The sums calculated are listed below. The error between the each of the last three sums and the actual value (as given by the calculator's function integration feature) is also given.

Left-Hand Sum : Left-hand sum
Right-Hand Sum : Right-hand sum
Midpoint Rule : Midpoint rule sum
Trapezoid Rule : Trapezoid rule sum
Simpson's Rule : Simpson's rule sum

Note: This program uses the calculator's 'Y0' graphing function in it's calculations, and will overwrite any equation previously stored there.

Using the Program:

The following example demonstrates the use of the program to give an approximate solution to the integral 1D Riemann Sum.

Screen Shot
1) Start the program. The screen depicted at right will appear. Press 'Enter'. Rmn1D Screenshot 1
2) The next screen contains instructions, as shown at right. Press 'Enter'. Rmn1D Screenshot 2
3) Enter the function after the 'F(X) = ' prompt, as shown. Press 'Enter'. Rmn1D Screenshot 3
4) Prompts for upper and lower limits of integration appear, followed by a prompt for the number of subdivisions to use in the calculation. (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. Rmn1D Screenshot 4
5) After a delay (the length of which depends on the number of subdivisions calculated), the results are presented as at right. The Left-Hand and Right-Hand sums are at the top, followed by the Trapezoid Rule result and the difference between it and the actual value, the Midpoint Rule result and it's error, and finally the Simpson's Rule result and it's error. When you're ready to continue, press 'Enter'. Rmn1D Screenshot 5
6) Press '2' at this point to quit, and the program exits. Pressing '1' results in the next screen being presented. Rmn1D Screenshot 6
7) 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. Rmn1D Screenshot 7

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