David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735

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The Riemann Integral

The following applet approximates the net area between the x-axis and the curve y=f(x) for a ≤ x ≤ b using Riemann Sums. Simply enter the function f(x), the values a, b and 0 ≤ n ≤ 500, the number of subintervals. In this case, the applet randomly breaks up the interval [a,b] into n subintervals and selects a value on each interval used to determine the height of the corresponding rectangle. The width and height of each rectangle can be manually adjusted by first clicking on the rectangle and then adjusting the corresponding points on the x-axis.

The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.

© 2010 David P. Little
Download this applet for off-line viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems