Use the Fundamental Theorem of Calculus to evaluate definite and indefinite integrals and to represent particular antiderivatives. Perform analytical and graphical analysis of functions so defined.


The Fundamental Theorem

by Allen Wolmer

Mooculus Calculus Textbook Section 13.1 pp 208-213

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A Youtube Calculus Workbook (Part 1). A guide through a playlist of instructional Calculus Videos. 

Section 16.1 pp 222-224

The first time you access this link to download the PDF, you will be asked four questions. Any that do not apply to you may be answered using any of the options listed.

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Instructional video from NROC/Hippocampus on the Antiderivative and Indefinite Integration from the Phoenix College Collection -Calculus II.

Video duration: 10:23

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Instructional video from NROC/Hippocampus on the Antiderivative and Indefinite Integration, Additional Examples from the Phoenix College Collection-Calculus II.

Video duration:  6:22

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Instructional video from NROC/Hippocampus on Definite Integrals and the Fundamental Theorem of Calculus from the Phoenix College Collection-Calculus II.

Video duration:  10:22

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Instructional video from NROC/Hippocampus on How to Determine the Value of a Definite Integral on the Graphing Calculator from the Phoenix College Collection-Calculus 1. 

Video duration:  4:09

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A Firefly Lectures video on this topic.

Video duration:  5:19

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A Firefly Lectures video on this topic.

Video duration:  4:13

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A Firefly Lectures video on this topic.

Video duration:  4:25

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A Firefly Lectures video on this topic.

Video duration:  5:43

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A Math League of America video on this topic.

Video duration:  18:23

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A Math League of America video on this topic.

Video duration:  10:09

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A Math League of America video on this topic.

Video duration:  14:48

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Mooculus Calculus Textbook Exercises, Sect 13.1 p 214 (Ans p 254)

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 3 Construct viable arguments and critique the reasoning of others.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
  • 8 Look for and express regularity in repeated reasoning.
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This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
  • 8 Look for and express regularity in repeated reasoning.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 4 Model with mathematics.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
Curriki RatingNR

This set of exercises supports the following Standards of Mathematical Practice

  • 1 Make sense of problems and persevere in solving them.
  • 2 Reason abstractly and quantitatively.
  • 5 Use appropriate tools strategically.
  • 6 Attend to precision.
  • 7 Look for and make use of structure.
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