David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Riemann Sums and the Area Under a Curve
The following applet approximates the net area between the xaxis 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 ≤ 10,000, the number of subintervals. You may select among Left Riemann Sums, Right Riemann Sums, the Midpoint Rule, the Trapezoidal Rule and Simpson's Rule to approximate the area. 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 xaxis in radians (i.e. multiples of pi), click on the graph and press "controlr". To switch back, simply press "controlr" again. Here is a list of functions that can be used with this applet.
© 2005 David P. Little Download this applet for offline viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 