Module 16 - The Fundamental Theorem
  Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test

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

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