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\nAP Calculus AB Unit 6: Integration and Accumulation of Change\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nThe 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,...\n
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\n\n38\nItems in Topic\n\n
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\nAP Calculus AB\n

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\n\nFor Students\n\n11th - 12th\n
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\nPrepare 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...\n
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Instructional Video1:47
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\nThe Second Fundamental Theorem of Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nHow 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...\n
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Instructional Video11:57
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\nPart 1 of the Dreaded Fundamental Theorem of Calculus!\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUse 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...\n
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AP Test Prep16:40
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\nCalculus AB/BC - The Fundamental Theorem of Calculus and Definite Integrals\n

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\n\nFor Students\n\n10th - 12th\n
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\nLearning 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...\n
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AP Test Prep11:54
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\nCalculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions\n

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\nConnect 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...\n
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\nHistorical Reflections on the Fundamental Theorem Of (Integral) Calculus\n

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\nHighlight 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...\n
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Instructional Video20:46
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\nIntegration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIntegrate 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...\n
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\nFundamental Theorem of Calculus Part 2\n

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\nUse 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...\n
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\nThe Second Fundamental Theorem of Calculus\n

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\nStudents 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.\n
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\nThe Fundamental Theorem of Calculus and Properties of the Definite Integral\n

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\nYoung 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...\n
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\nThe Fundamental Theorem of Calculus and Area Under the Curve\n

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\nTwelfth graders review the fundamental theorem of calculus and solve for the area under the curve. In this calculus lesson, 12th graders differentiate between the area under the curve and the definite integral as it related to the...\n
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\nNine Definite Integrals and Fundamental Theorem Of Calculus Problems\n

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\nIn 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...\n
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\nBasic Calculus II: Fundamental Theorem of Calculus\n

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\nIn this fundamental theorem learning exercise, students find the antiderivative of a function. This two page learning exercise contains five multi-step problems.\n
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\nFundamental Theorems of Mathematics\n

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\n\nFor Teachers\n\n9th - Higher Ed\n
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\nThere 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...\n
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\nApplied Fundamental Theorem of Calculus\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nHigh schoolers apply the Fundamental Theorem of Calculus. In this calculus activity, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.\n
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\nChallenge Sheet 2: Evaluate Functions\n

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\nIn this function instructional activity, students evaluate integrals using the fundamental theorem of calculus. They identify the maxima and minima on intervals. This one-page instructional activity contains seven problems.\n
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Handout
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\nStudy Guide for the Advanced Placement Calculus AB Examination\n

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\nIs 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...\n
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\nFundamental Theorem of Calculus Part 3\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this math worksheet, students read the examples of the fundamental theorem of calculus. They apply it in the form of a quiz.\n
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\nPart 3 of the Fundamental Theorem of Calculus\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Fundamental Theorem of Calculus worksheet, students find the solution of given functions. This one-page worksheet contains five problems.\n
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\nUnderstanding the Fundamental Theorem of Calculus\n

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\nIn this Fundamental Theorem of Calculus worksheet, students demonstrate their understanding of the theorem by identifying the derivative and anti-derivative of given functions. This two-page worksheet contains ten problems.\n
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\nThe First Fundamental Theorem of Calculus\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nSolve problems using the fundamental theorem. In this calculus lesson, high schoolers solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.\n
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\nFundamental Theorem of Calculus\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nHigh schoolers, with the assistance of their TI-84 Plus / TI-83 Plus calculators, explore and assess the connections between an accumulation function, one defined by a definite integral, and the integrand. They summarize that the...\n
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Worksheet
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\nFundamental Theorem of Calculus\n

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\n\nFor Students\n\n11th - 12th\n
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\nFor this calculus worksheet, students observe the graph the function and identify the interval as increasing or decreasing. They identify the critical points and perform integration. There are 4 questions.\n
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