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\n\"The\n\n
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\nThe Second Fundamental Theorem of Calculus\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nYoung scholars investigate the fundamental theorem of calculus. For this calculus lesson, students derive the fundamental theorem of calculus. They differentiate between the first and second theorem.\n
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\n\"Fundamental\n\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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Lesson Plan
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\n\"Elevator\n\n
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\nCurated OER\n
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\nElevator Height as Integral of Velocity\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nPupils investigate integrals and their relationship to velocity in this calculus lesson. They use the idea of a moving elevator to explore vertical motion and use the TI to help them create a visual.\n
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Lesson Plan
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\n\"The\n\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, students solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.\n
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\n\"Integration\n\n
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\nTexas Instruments\n
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\nIntegration By Parts\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nPupils solve problems using integration by parts in this calculus lesson. Learners apply the product rule and integration by parts. They graph the equation and use the TI to observe the integration process.\n
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\n\"AP\n\n
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\nCurated OER\n
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\nAP Calculus Exam Prep\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nPupils practice sample questions from the AP Calculus Exam. They solve calculus problems involving bounded regions, integration, derivatives, and limits. They then answer free response and multiple choice questions on the above mentioned...\n
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Lesson Planet Article
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\n\"Exploring\n\n
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\nCurated OER\n
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\nExploring Functions with Calculus and Dynamic Software\n

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\n\nFor Teachers\n\n11th - Higher Ed\n
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\nCalculus can be project-based and inquiry-centered by using dynamic software.\n
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Unit Plan
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\n\"Module\n\n
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\nMathematics Vision Project\n
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\nModule 4: Linear and Exponential Functions\n

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\n\nFor Teachers\n\n8th - 10th\n\nStandards\n
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\nSequences and series are traditionally thought of as topics for the pre-calculus or calculus class, when learners are figuring out how to develop limits. But this unit uses patterns and slopes of linear functions in unique ways...\n
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Worksheet
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\n\"Calculating\n\n
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\nCurated OER\n
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\nCalculating Arc Lengths of Simple Functions-I\n

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\n\nFor Students\n\n10th - Higher Ed\n
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\nIn this calculating arc lengths worksheet, students are given 4 simple functions and they use the Pythagorean Theorem and the basic techniques of calculus to find the arc-length formula in order to find the arc-length.\n
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\n\"MVT\n\n
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\nMVT for Integrals\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nStudents identify the meaning of the Mean Value Theorem. In this calculus instructional activity, students solve problems using the definite integral. They calculate the average value of a function.\n
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\n\"Exploration\n\n
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\nExploration 3: Introduction to Definite Integrals\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn this integral worksheet, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page worksheet contains approximately 40 problems.\n
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Interactive
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\n\"Categorize\n\n
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\nCurated OER\n
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\nCategorize Twelve Integrals\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this integral worksheet, learners categorize the given twelve integrals to determine which of the four basic integral functions provided each follows.\n
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\n\"Exploration\n\n
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\nExploration 4: Definite Integrals by Trapezoidal Rule\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this integral worksheet, students geometrically estimate distance in given problems. They use the trapezoidal rule to determine definite integrals. Students explore distance and velocity. This three-page worksheet contains...\n
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Lesson Plan
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\n\"The\n\n
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\nThe Fundamental Theorem of Calculus and Properties of the Definite Integral\n

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\n\nFor Teachers\n\n11th - Higher Ed\n
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\nLearners discuss the importance of fundamental theorems in math. In this calculus lesson plan, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how...\n
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\n\"Functions\n\n
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\nFunctions Defined by Integrals\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this calculus worksheet, students solve functions by taking the derivative of the function. There are 3 questions with and answer key.\n
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Worksheet
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\n\"Fundamental\n\n
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\nFundamental Theorem of Calculus\n

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\n\nFor Students\n\n11th - 12th\n
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\nIn 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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\n\"Inverse\n\n
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\nInverse Trigonometric Functions (Review)\n

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\n\nFor Teachers\n\n11th - Higher Ed\n
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\nStudents discuss the importance of inverse functions and derivatives. In this calculus lesson, students analyze inverse trig functions by solving for missing angles. They graph the functions and discuss integration by parts.\n
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\n\"Calculus\n\n
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\nCalculus Exam\n

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\n\nFor Students\n\n11th\n
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\nIn In this calculus worksheet, student solve 6 multi-step problems involving volume, intervals, acceleration, and graphing. A graphing calculator will be necessary to complete the worksheet.\n
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\nThe Definite integral and Area Under a Curve\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents define integrals and explore how they relate to the areas under a curve. For this calculus lesson, students solve word problems relating curves and integrals. They sing a song to help them remember the formula for the area under...\n
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\n\"Integrals\n\n
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\nCurated OER\n
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\nIntegrals involving Trig Substitution\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents define integrals and list the trig values. In this calculus instructional activity, students integrate functions using trig substitution. They solve integrals containing sums and differences of squares.\n
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Worksheet
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\n\"AP\n\n
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\nCurated OER\n
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\nAP Calculus Practice Exam\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this calculus worksheet, students calculate the derivative, find the invertible given the derivative and review basic concepts for their AP calculus exam. There are 17 questions.\n
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\n\"Integration\n\n
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\nIntegration Involving Inverse Trig Functions\n

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\n\nFor Teachers\n\n12th - Higher Ed\n
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\nLearners review the steps for integration and solve equations using integration by parts. In this calculus lesson, students apply their knowledge of integration to inverse trig function. Learners review their trig and inverse trig...\n
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\n\"Integration\n\n
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\nIntegration By Parts\n

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\n\nFor Teachers\n\n12th\n
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\nTwelfth graders define integration by parts and solve integrals. In this calculus lesson, 12th graders integrate functions using the product rule. They work example problems with the teacher before doing it on their own.\n
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\n\"Average\n\n
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\nAverage Value of a Function\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents investigate the average value of a function given different interval values. For this calculus lesson, students explore word problems and apply their knowledge of average value to find the answer. They apply previous knowledge...\n
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