Domain: Calculate and Apply Integrals Objectives: 7.2: Volume: The Disk Method Section Project (after 7.3) Apply integrals to solve problems Students will: 7.3: Volume: The Shell Method Cluster: Find the volume of a solid of revolution using the disk method. Additional Resource(s) Use a definite integral to find the volume of a formed by rotating around a Find the volume of a solid of revolution Larson Calculus Videos Section 7.2 – given axis. using the washer method. Larson Calculus Videos Section 7.3 – Find the volume of a with a known cross section. Find the volume of a solid of revolution Khan Academy Calculus Videos using the shell method. See engageny Lesson for Exit Compare the uses of the disk method and Ticket/Discussion Questions. the shell method. Understanding Integrals 4.3: Riemann Sums and Definite Integrals Domain: Objectives: Writing in Math/Discussion Cluster: Demonstrate understanding of a Students will: Give an example of a function that is Definite Integral Additional Resource(s) integrable on the interval [-1, 1], but not Understand the definition of Riemann continuous on [-1, 1] sums. Larson Calculus Videos Section 4.3 – Define the definite integral as the of Evaluate a definite integral using limits. Riemann sums and as the net Evaluate a definite integral using accumulation of change. properties of definite integrals. Khan Academy Calculus Videos Correctly write a Riemann sum that represents the definition of a definite integral. Domain: Understanding Integrals Objectives: 4.4: The Fundamental Theorem of Calculus Writing in Math/Discussion Cluster: Understand and apply the Students will: Research and prepare a report on the Fundamental Theorem of Calculus Additional Resource(s) Fundamental Theorem of Calculus and the Evaluate a definite integral using the mathematicians Newton and Gottfried Fundamental Theorem of Calculus. Leibniz. Larson Calculus Videos Section 4.4 – Evaluate definite integrals the Understand and use the Mean Value Fundamental Theorem of Calculus. Theorem for integrals. Use the Fundamental Theorem of Find the average value of a function over Calculus to represent a particular a closed interval. Khan Academy Calculus Videos antiderivative of a function and to
Domain: Calculate and Apply Integrals Cluster: Apply integrals to solve problems Use a definite integral to find the volume of a formed by rotating around a given axis. Objectives: Students will: Find the volume of a solid of revolution using the disk method. Find the volume of a solid of revolution using the washer method. Find the volume of a with a known cross section. Find the volume of a solid of revolution using the shell method. Compare the uses of the disk method and the shell method. 7.2: Volume: The Disk Method 7.3: Volume: The Shell Method Additional Resource(s) Larson Calculus Videos – Section 7.2 Larson Calculus Videos – Section 7.3 Khan Academy Calculus Videos Section Project (after 7.3) See engageny Lesson for Exit Ticket/Discussion Questions. Domain: Understanding Integrals Cluster: Demonstrate understanding of a Definite Integral Define the definite integral as the of Riemann sums and as the net accumulation of change. Correctly write a Riemann sum that represents the definition of a definite integral. Objectives: Students will: Understand the definition of Riemann sums. Evaluate a definite integral using limits. Evaluate a definite integral using properties of definite integrals. 4.3: Riemann Sums and Definite Integrals Additional Resource(s) Larson Calculus Videos – Section 4.3 Khan Academy Calculus Videos Writing in Math/Discussion Give an example of a function that is integrable on the interval [-1, 1], but not continuous on [-1, 1] Domain: Understanding Integrals Cluster: Understand and apply the Fundamental Theorem of Calculus Evaluate definite integrals the Fundamental Theorem of Calculus. Use the Fundamental Theorem of Calculus to represent a particular antiderivative of a function and to Objectives: Students will: Evaluate a definite integral using the Fundamental Theorem of Calculus. Understand and use the Mean Value Theorem for integrals. Find the average value of a function over a closed interval. 4.4: The Fundamental Theorem of Calculus Additional Resource(s) Larson Calculus Videos – Section 4.4 Khan Academy Calculus Videos Writing in Math/Discussion Research and prepare a report on the Fundamental Theorem of Calculus and the mathematicians Newton and Gottfried Leibniz.
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