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Calculus I–III by Topic
/ Chapter 9 · Applications of Integration
Section 9.5
Areas of Surfaces of Revolution
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Calculus I–III by Topic
Ch 1 · Review and Prerequisites
1.1 Functions, Graphs, and Lines Review
1.2 Exponential and Logarithmic Functions Review
1.3 Trigonometry Review
1.4 Equations, Inequalities, and Algebra Review
1.5 Exponents and Logarithms
1.6 Factoring
1.7 Functions, Graphs, and Lines
1.8 Algebraic Manipulation and Calculus Prep
Ch 2 · Limits and Continuity
2.1 Introduction to Calculus
2.2 Introduction to Limits
2.3 The Formal Definition of the Limit
2.4 One-Sided Limits
2.5 Introduction to Continuity
2.6 Infinite Limits and Limits at Infinity
2.7 Study & Exam Review
Ch 3 · Differentiation
3.1 Introduction to the Derivative
3.2 Basic Derivative Rules
3.3 Position, Velocity, and Acceleration
3.4 Trigonometric Derivatives
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Derivatives of General Exponential and General Logarithmic Functions
3.8 Derivatives of Inverse Trig Functions
3.9 Related Rates Problems
3.10 Linearization
3.11 Study & Exam Review
Ch 4 · Applications of the Derivative
4.1 Extreme Values on Closed Intervals and Critical Points
4.2 Rolle's Theorem and the Mean Value Theorem
4.3 The First Derivative Test for Extrema
4.4 Graphing
4.5 L'Hopital's Rule
4.6 Optimization
4.7 Newton's Method
4.8 Antiderivatives
4.9 Study & Exam Review
Ch 5 · Integration
5.1 Area Estimates and Riemann Sums
5.2 Sigma Notation and the Definite Integral as a Limit of Riemann Sums
5.3 Definite Integrals Using Known Area Formulas
5.4 The Fundamental Theorem of Calculus
5.5 The Substitution Method with Indefinite Integrals
5.6 The Substitution Method with Definite Integrals
5.7 Study & Exam Review
Ch 6 · Transcendental Functions and Separable Differential Equations
6.1 The Logarithm Defined as an Integral
6.2 Separable Differential Equations and Exponential Growth or Decay
6.3 Hyperbolic Functions
Ch 7 · Study Series (Exam Preparation)
7.1 Limits and Continuity Series
7.2 Derivative Rules Series
7.3 L'Hopital's Rule
7.4 Maximums/Minimums/Concavity Etc
7.5 Integration Series
Ch 8 · Review of Integration (from Calculus I)
8.1 Antiderivatives and Indefinite Integrals
8.2 Definite Integrals
8.3 The Substitution Method with Indefinite Integrals
8.4 The Substitution Method with Definite Integrals
Ch 9 · Applications of Integration
9.1 The Area Between Two Curves
9.2 Finding Volume Using the Disk Method or Washer Method
9.3 Finding Volume Using the Cylindrical Method
9.4 Finding Arc Length Using Integration
9.5 Areas of Surfaces of Revolution
9.6 Variable Force Applications
Ch 10 · Techniques of Integration
10.1 Review of Integration Techniques
10.2 Integration by Parts
10.3 Integrating with Trigonometric Functions
10.4 Trigonometric Substitution
10.5 Partial Fractions
10.6 The Trapezoidal Rule
10.7 Improper Integrals
Ch 12 · Sequences and Series
12.1 Sequences
12.2 Infinite Series
12.3 The Integral Test for Series
12.4 Comparison Tests for Series
12.5 Absolute Convergence and the Ratio and Root Tests
12.6 The Alternating Series Test and Conditional Convergence
12.7 Power Series
12.8 Taylor and Maclaurin Series
12.9 Convergence of Taylor Series and Operations on Power Series
12.10 Binomial Series and Other Power-Series Applications
Ch 13 · Parametric Equations and Polar Coordinates
13.1 Parametrization of Plane Curves
13.2 Calculus with Parametric Curves
13.3 Polar Coordinates
13.4 Graphing in Polar Coordinates
13.5 Areas and Lengths in Polar Coordinates
Ch 14 · Vectors and the Geometry of Space
14.1 Three-Dimensional Coordinate Systems
14.2 Vectors
14.3 The Dot Product
14.4 The Cross Product
14.5 Lines and Planes in Space
14.6 Cylinders and Quadric Surfaces
Ch 15 · Vector-Valued Functions and Motion in Space
15.1 Curves in Space and Their Tangents
15.2 Integrals of Vector Functions
15.3 Arc Length in Space
15.4 Curvature and Normal Vectors of a Curve
15.5 Tangential and Normal Components of Acceleration
Ch 16 · Partial Derivatives
16.1 Functions of Several Variables
16.2 Limits and Continuity in Higher Dimensions
16.3 Partial Derivatives
16.4 The Chain Rule
16.5 Directional Derivatives and Gradient Vectors
16.6 Tangent Planes and Differentials
16.7 Extreme Values and Saddle Points
16.8 Lagrange Multipliers
Ch 17 · Multiple Integrals
17.1 Double and Iterated Integrals over Rectangles
17.2 Double Integrals over General Regions
17.3 Areas by Double Integration
17.4 Double Integrals in Polar Form
17.5 Triple Integrals in Rectangular Coordinates
17.6 Triple Integrals in Cylindrical and Spherical Coordinates
17.7 Substitutions in Multiple Integrals
Divide and Conquer Math
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