An Area Between Curves Applet

One of the standard applications of the definite integral is to find the area between two curves.  To find the area you need to have two curves that bound the area and limits of integration.

This can be set up where the region of integration is defined with a top curve and a bottom curve.  In this case we have a range of integration for x.  For each x we use the difference between the top and bottom curves as the integrand.
The problem can also be set up with the area defined as going from a left curve to a right curve with a range of integration for y.

Things to notice:
• The view window for the graph is defined by the ordered pairs xWindow and yWindow.
• The boundary curves are graphed in green.  A pair of green and blue dots  are graphed at the  value of t0 on the low and high curves respectively.  The numeric values of these points can be found in a readout on the control panel.
• In either direction the area can be thought of as broken into very thin rectangles that are so thin they look like lines.
• The arrows should go either from bottom to top or from left to right.  If the arrows go the other way the integrand is negative.
• The value of area in the readout is found using Simpson's rule with 20 subdivisions.

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.