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 



Area Between Curves
The following applet approximates the area between the curves y=f(x) and y=g(x) for a ≤ x ≤ b using Riemann Sums. Simply enter the functions f(x) and g(x) and the values a, b and 0 ≤ n ≤ 10,000, the number of subintervals. The height of each rectangle is computed using the midpoint rule and taken to be f(x)  g(x). In other words, it does not matter which function is the larger of the two. 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 The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 