# Fundamental Theorem of Calculus Teacher Resources

Find Fundamental Theorem of Calculus lesson plans and worksheets

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#### AP Calculus AB Unit 6: Integration and Accumulation of Change

The 14 lessons in the AP Calculus AB Unit 6: Integration and Accumulation of Change use informative videos to introduce the topic of each lesson and model procedures. Each resource packet includes a video, worksheets, practice solutions,...

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#### AP Calculus AB

Prepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...

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#### The Fundamental Theorem of Calculus

Knowledge of definite integrals is fundamental to the understanding of calculus. Instructors of an AP® Calculus course consult a comprehensive guide to the Fundamental Theorem of Calculus. The document provides teaching suggestions and...

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#### The Second Fundamental Theorem of Calculus

How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...

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#### Fundamental Theorem of Calculus

Does it make more sense to teach the Second Fundamental Theorem of Calculus before the First Fundamental Theorem of Calculus? An AP® Calculus curriculum module explores the interesting question. A set of five worksheets first looks at...

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#### The Fundamental Theorems of Calculus

Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The...

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#### Part 1 of the Dreaded Fundamental Theorem of Calculus!

Use the Fundamental Theorem of Calculus to find a derivative. With an example, pupils observe how being to derive a formula to help determine the derivative of any given integral. The video derives the formula using the first part of the...

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#### Calculus AB/BC - The Fundamental Theorem of Calculus and Definite Integrals

New ReviewLearning about definite integrals is fundamental to any calculus course. The eighth of 16 parts in Unit 6 - Integration focuses on the Fundamental Theorem of Calculus. Scholars first see how to find antiderivatives, then discover how to...

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#### Calculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions

Connect integrals with differentiation. The beginning of the video introduces the definition of an accumulation function. Scholars learn about the relationship between integrals and derivatives. Using what is commonly known as Part Two...

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#### Historical Reflections on the Fundamental Theorem Of (Integral) Calculus

Highlight the process of mathematical discovery for your classes. This lesson examines the development of the Fundamental Theorem of Calculus over time. Understanding the history of the theorem helps create a better understanding of the...

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#### Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8

Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance helps...

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#### Fundamental Theorem of Calculus Part 2

Use the Fundamental Theorem, not just look at it. Learners watch as the video walks viewers through finding the definite integral of a trigonometric function. The presenter provides helpful suggestions as she evaluates the example...

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#### The Area Function

Students explore the concept of area under a curve. In this area under a curve lesson, students find integrals of various functions. Students use their Ti-Nspire to graph functions and find the area under the curve using the...

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#### Accumulation Functions

Twelfth graders explore functions defined by a definite integral. In this Calculus activity, 12th graders investigate accumulation functions in which a variable is a limit of integration. The activity is meant to be an introduction to...

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#### The Fundamental Theorem of Calculus and Properties of the Definite Integral

Young scholars discuss the importance of fundamental theorems in math. In this calculus instructional activity, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems...

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#### The Second Fundamental Theorem of Calculus

Learners investigate the fundamental theorem of calculus. In this calculus lesson, students derive the fundamental theorem of calculus. They differentiate between the first and second theorem.

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#### The Fundamental Theorem of Calculus and Area Under the Curve

Twelfth graders review the fundamental theorem of calculus and solve for the area under the curve. In this calculus lesson plan, 12th graders differentiate between the area under the curve and the definite integral as it related to the...

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#### Nine Definite Integrals and Fundamental Theorem Of Calculus Problems

In this definite integral worksheet, student find the value of five definite integrals. Student then explain why a definite integral inequality holds true. Finally, students are given the graph of a functions and asked to determine...

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#### Basic Calculus II: Fundamental Theorem of Calculus

In this fundamental theorem worksheet, students find the antiderivative of a function. This two page worksheet contains five multi-step problems.

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#### Fundamental Theorems of Mathematics

There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true.

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#### The Fundamental Theorem of Calculus

Practice in the mechanics of using substitution in integration is often hard to come by in enough quantity for learners to really wrap their heads around the nuances of the technique. This worksheet set with solution key and worked...

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#### Applied Fundamental Theorem of Calculus

Students apply the Fundamental Theorem of Calculus. In this calculus lesson, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.

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#### Challenge Sheet 2: Evaluate Functions

In this function worksheet, students evaluate integrals using the fundamental theorem of calculus. They identify the maxima and minima on intervals. This one-page worksheet contains seven problems.

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#### Study Guide for the Advanced Placement Calculus AB Examination

Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and integral calculus,...