MATH 1501: WEEK 9

Topics for this week are:

• The definite integral
• The fundamental theorem of calculus
• Computation of the area under a graph

Text coverage:     Sections 5.1 - 5.4 of Salas, Hille, and Etgen

Online resources:

• Maple Worksheets
  • Area by Chance: The Riemann integral is usually defined as the limit of a collection of approximating sums. There after, the fundamental theorem of integral calculus provides methods for evaluating integrals without computing limits of sums. As an alternative idea, this worksheet introduces a random number generator and what is usually called "Monte-Carlo Techniques" to evaluate integrals. "Area by Chance" is a good worksheet to examine early in the introduction of the integral.
• Java Projects
  • Riemann sums for integrals of a single variable: This applet is designed for experimenting with Riemann Sums and with numerical integration. It can be used to check the results of a computation of a definite integral.

---

Last Modified: . School of Mathematics, Georgia Institute of Technology.