The Riemann program calculates the left-hand, right-hand, trapezoid, midpoint, and Simpson Riemann sums which are commonly used to estimate the value of a single definite integral of a reasonably well-behaved real-valued function.

This program provides

the calculated sums' values. If you wish to view a graphical display of the geometry used for each sum, use the aplet called 'RSum' instead.ONLY

- To begin, enter the integrand into the F1(X) slot in the symbols mode. (The integrand MUST be F1(X)!):

- Start the program RIEMANN from the Program menu.
- Read the instructions that appear. Notice that each of the sums calculated is stored (for later use) in the variable named. When you are ready to proceed, press any key.
- When the input screen appears, enter the left (H-MIN) and right (H-MAX) limits of integration followed by the number of subintervals (# OF SUBS) to be used. These must be enclosed in braces and must be entered in precisely this order: {H-MIN, H-MAX, # OF SUBS}. For example, to integrate from 2 to 5 using 13 subintervals, you would enter
**{**2,5,13**}**. - The various Riemann sums will be displayed in succession. When you are ready to view the next, press the 'OK' key (upper right-hand corner).