Module 16 - The Fundamental Theorem Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test Introduction In the previous module you defined left and right Riemann sums and used these sums to find the area under the curve f(x) = x2 from x = 0 to x = 1. In this module you will use Riemann sums to find other areas and discover the remarkable connection between areas under a curve and derivatives called the Fundamental Theorem of Calculus. Although you will discover this theorem in the context of finding areas under a curve, it is used in a wide variety of applications extending far beyond finding areas. Lesson Index: 16.1 - Area Functions, A Symbolic Approach 16.2 - Area Functions, A Visual Approach 16.3 - The Fundamental Theorem of Calculus After completing this module, you should be able to do the following: Describe the Fundamental Theorem of Calculus using a symbolic approach Recognize the Fundamental Theorem of Calculus in a graphical setting Use the Fundamental Theorem of Calculus to evaluate definite integrals and find areas Visualize the general shape of an area function by using characteristics of the curve function Use the Fundamental Theorem of Calculus to differentiate functions defined by integrals Next > ©Copyright 2007 All rights reserved. | Trademarks | Privacy Policy | Link Policy