Math 131 Calculus II: Riemann Sums


To compute a Riemann sum, select "Riemann Sums Utility" from the menu at the top. Additional instructions below.


Quick Instructions

General: When the applet starts up, it is showing a "Main Screen" where you can see the graph of functions. The available functions are shown in a list on the left. Click on a function to view its graph. You can define your own functions to add to this list using the three buttons at the lower left of the Main Screen. There are three ways to define new functions: using expressions (such as 0.5*x^2+sin(3*x-2)), by giving the graph of the function, or by listing a table of (x,y) pairs. There is a separate input screen for each of these input methods. Note: The square root function can be entered as either sqrt(x) or x^(1/2). To get back to the Main Screen from one of these input screens, you have to press a "Done" or "Cancel" button. The pop-up menu at the top of the applet can be used to go to seven other screens. Each screen is a separate "utility" that allows you to play with functions in a different way. When you enter functions into the utility screens, you can use any new functions that you have defined, as well as the built-in functions.

You'll also find some extra entries in the pop-up menu. These extra entries are examples that will you take to one of the utility screens, and load an example in to that screen.

Riemann Sums: To use the applet to compute a Riemann sum, use the pull-down menu at the top of the applet and select "Riemann Sums Utility". In the spaces provided, fill in the max and min values of x and y, number of intervals or partitions n, and enter the function f(x). Select the type of summation you want to display (e.g., right endpoint). Note that several different sums will be calculated, but only the selected one is drawn. Finally, remember to press the "Compute" button to re-calculate the sums.

Now, just go ahead and play!


The applet on this page as developed as part of the
Java Components for Mathematics Project
at Hobart and William Smith Colleges.

Special thanks to David Eck.

This project was supported by NSF grant number DUE-9950473.


Hobart and William Smith Colleges: Department of Mathematics and Computer Science