# Activities

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• • ##### Subject Area

• Math: Calculus: Fundamental Theorem

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

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The First Fundamental Theorem of Calculus

#### 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.