Integration is an important calculus topic that has a variety of applications. Area is one of the most important applications of the definite integral. However, the boundaries of some regions are irregular, and it is therefore difficult to create a definite integral that will closely approximate the region's area. The state of Virginia is one such region.
In this project you will use Riemann sums and the computer algebra system MAPLE to begin your investigation of the area of a complex region. More specifically you will mark boundary points on a map of Virginia (excluding the Eastern Shore) and then import their coordinates to a MAPLE worksheet. You will then learn the MAPLE commands for plotting these points and the rectangles, trapezoids, and parabolas they define. In addition you will use MAPLE to find the area of these sub-regions and to approximate the total area.
|Julie Clark, Caren Diefenderfer, and Trish Hammer are in the Department of Mathematics and Statistics at Hollins University. Steve Hammer is in the Department of Mathematics at Virginia Western Community College.|