Education Technology

The First Fundamental Theorem of Calculus

Published on 03/16/2011

Activity Overview

Make visual connections between a function and its definite integral.

Objectives

  • Students will be able to identify the graphical connections between a function and its accumulation function.
  • Students will be able to describe the relationship between a function and its accumulation function.
  • Students will be able to apply and explain the first Fundamental Theorem of Calculus.
  • Use appropriate tools strategically. (CCSS Mathematical Practice)
  • Look for and express regularity in repeated reasoning. (CCSS Mathematical Practice)

Vocabulary

  • Signed area
  • Accumulation function
  • Local maximum
  • Local minimum
  • Inflection point

About the Lesson

The intent of this lesson is to help students make visual connections between a function and its definite integral. As a result, students will:

  • Observe the coincidence of the accumulation function’s extrema with the original function’s zeros, and of the accumulation function’s inflection point with the original function’s extremum.
  • Solidify understanding of the relationship between the derivative of the accumulation function and the original function.
  • Conclude with explicitly stating the first Fundamental Theorem of Calculus.