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.

To complete this project you should work through each of the links below.

## 1. Learning to Use the Virginia State Map## 2. Using Left Rectangles## 3. Using Right Rectangles## 4. Using Trapezoids## 5. Using Simpson's Rule## 6. Project Assignment |

* Department of Mathematics, Virginia Western Community College

Last updated February 23, 2011 12:29 PM