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Home › Courses › Calculus 1/AB/BC › Archive for Chapter 7 – Area, Volume, and Arc Length
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Chapter 7 – Area, Volume, and Arc Length

This Chapter starts with a master class in how to find the area of a bounded region and the area between two curves.  Next, you will make simple work of how to set up and solve integrals to find the volume of solids of revolution using the Disk and Washer methods.  From there you will see the beauty of simple geometry come alive when you master finding volumes of solids with cross-sections.  You will then rock how to find volumes of solids of revolution using the Shell Method.  After this, you will explore the concepts of arc length and surface area.  The chapter wraps up with original AB and BC free response questions that incorporate many of the above topics.  Time to see how basic geometry with a little Calculus can make for some awesome concepts!

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Lesson 1 – Area Between Two Curves

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Lesson 1 – Area Between Two Curves (Part 2)

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods (Part 2)

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Lesson 2 – Volume of Solids of Revolution: Disk and Washer Methods (Part 3)

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Lesson 3 – Volumes of Solids with Known Cross-Sections

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Lesson 4 – The Shell Method

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Lesson 5 – Arc Length and Surface Area

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Lesson 6 – AB and BC Exam Practice Problems

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      • 6th Grade Math
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Whole Numbers & Decimals
        • Chapter 2: Representing Data In Different Ways
        • Chapter 3: Variables, Algebraic Expressions, & Solving Equations
        • Chapter 4: Divisibility, Factoring Numbers, & Fractions
        • Chapter 5: Addition and Subtraction of Fractions
        • Chapter 6: Multiplication and Division of Fractions
        • Chapter 7: Ratios, Proportions, and Percents
        • Chapter 8: Fundamentals of Geometry
        • Chapter 9: Unit Conversions, Perimeter, Area, & Volume
        • Chapter 10: Introduction to Probability
        • Chapter 11: Integers – Properties, Operations, & Equations
        • Chapter 12: Two-Step Equations and Inequalities
      • Pre-Algebra
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions & Operations with Integers
        • Chapter 2: One-Step Equations & Inequalities
        • Chapter 3: Operations and Equations With Decimals
        • Chapter 4: Factors, Simplifying Fractions, and Exponent Rules
        • Chapter 5: Fraction Operations & Solving Equations with Fractions
        • Chapter 6: Operations and Uses of Ratios, Proportions, & Percents
        • Chapter 7: Solving Equations and Inequalities
        • Chapter 8: Relations & Functions, Slope, Lines, and Graphing
        • Chapter 9: Foundations of Geometry
        • Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume
        • Chapter 11: Right Triangles and An Introduction to Trigonometry
        • Chapter 12: Data Analysis: Techniques and Calculations
        • Chapter 13: Probability, Combinations, and Permutations
        • Chapter 14: Foundations of Non-Linear Functions and Polynomial Operations
      • Algebra 1
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions and Operations with Real Numbers
        • Chapter 2: Solving Equations – From One-Step to Multi-Step
        • Chapter 3: Ratios, Proportions, & Percents
        • Chapter 4: Solving Inequalities
        • Chapter 5: Introduction to Graphs and Functions
        • Chapter 6: Linear Functions and Graphing Lines
        • Chapter 7: Systems of Linear Equations and Linear Inequalities
        • Chapter 8: Exponent Rules & Exponential Functions
        • Chapter 9: Polynomials
        • Chapter 10: Graphing and Solving Quadratic Equations
        • Chapter 11: Introduction to Rational Expressions
        • Chapter 12: Radicals and An Introduction to Trigonometry
        • Chapter 13: Data Analysis: Techniques and Calculations
        • Chapter 14: Probability, Combinations, and Permutations
      • Calculus 1 & 2 / AB / BC
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1 – Limits
        • Chapter 2 – Derivatives
        • Chapter 3 – Uses of the Derivative
        • Chapter 4 – Integration
        • Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry
        • Chapter 6 – Differential Equations and Exponential & Logistic Growth
        • Chapter 7 – Area, Volume, and Arc Length
        • Chapter 8 – Advanced Integration Techniques and Improper Integrals
        • Chapter 9 – Series and Tests for Convergence and Divergence
        • Chapter 10 – Taylor Polynomials and Power Series
        • Chapter 11 – The Calculus of Parametric and Polar Equations
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