Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
Volumes of Solids Generated by Rotation: Shell Method
The following applet approximates the volume of the solid generated by rotating the region of the xy-plane bounded by the curves y=f(x) and y=g(x) for a ≤ x ≤ b about the vertical line x=A. Simply enter the functions f(x) and g(x) and the values a, b, A and 0 ≤ n ≤ 100, the number of subintervals.
The values a, b and A 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, dragging the corresponding point/line 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.
You can rotate the object about the center of the screen by dragging the mouse while holding down the SHIFT key.
Here is a list of functions that can be used with this applet.
© 2005 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