Education Technology

The Second Fundamental Theorem of Calculus

Published on 03/16/2011

Activity Overview

Students 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.
  • For a given function, students will recognize the accumulation function as an antiderivative of the original function.
  • Students will be able to apply and explain the second Fundamental Theorem of Calculus.
  • Construct viable arguments and critique the reasoning of others. (CCSS Mathematical Practice)
  • Look for and make use of structure. (CCSS Mathematical Practice)

Vocabulary

  • accumulation function
  • definite integral
  • antiderivative

About the Lesson

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

  • Students will use the accumulation function with a fixed starting point to find definite integrals of a function over different intervals.
  • Students will observe that the accumulation function is an antiderivative of the original function.
  • Students will apply the antiderivative property of the accumulation function in combination with their use of the accumulation function to determine a definite integral.
  • The lesson concludes with students stating and applying an informal statement of the second Fundamental Theorem of Calculus.
  • This lesson is designed to follow the lesson The First Fundamental Theorem of Calculus.