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MA101: Single-Variable Calculus I
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MA101: Single-Variable Calculus I
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Unit 8: Applications of Integration
8.1: The Area between Curves
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 4: Integration, Section 4.5: Areas between Two Curves"
Back to '8.1: The Area between Curves'
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University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 4: Integration, Section 4.5: Areas between Two Curves"
Read Section 4.5 (pages 218 through 222).
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◄ Unit 8 Learning Outcomes
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Course Syllabus
Course Terms of Use
Unit 1 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Section 1.1: Lines"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Exercises 1.1: Problems 1-18"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Section 1.2: Distance between Two Points; Circles"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Exercises 1.2, Problems 1, 2, 6"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Section 1.3: Functions"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Exercises 1.3, Problems 1-16"
Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web"
Whitman College: David Guichard's "Calculus, Chapter 1: Analytic Geometry, Section 1.4: Shifts and Dilations"
Unit 2 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.1: The Slope of a Function"
Massachusetts Institute of Technology: David Jerison's "Rate of Change"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Exercises 2.1, Problems 1 - 6"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.2: An Example"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Exercises 2.2, Problems 1 - 3"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.3: Limits"
Massachusetts Institute of Technology: David Jerison's "Limits"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Exercises 2.3, Problems 1 - 18"
University of California, Davis: Duane Kouba's "Precise Limits of Functions as x Approaches a Constant"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.3: A Hard Limit"
PatrickJMT: "The Squeeze Theorem for Limits"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.4: The Derivative Function"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative: Exercises 2.4, Problems 1 - 5, 8 - 11"
Whitman College: David Guichard's "Calculus, Chapter 2: Instantaneous Rate of Change: The Derivative, Section 2.5: Adjectives for Functions"
Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web"
Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web"
PatrickJMT: "Intermediate Value Theorem"
Unit 3 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Section 3.1: The Power Rule"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Exercises 3.1, Problems 1-6"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Section 3.2: Linearity of the Derivative"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Exercises 3.2, Problems 1 - 9, 11, 12"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Section 3.3: The Product Rule"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives: Exercises 3.3, Problems 1-5"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives: Section 3.4: The Quotient Rule"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives: Exercises 3.4, Problems 5, 6, 8, 9"
Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Section 3.5: The Chain Rule"
Massachusetts Institute of Technology: David Jerison's "Chain Rule"
Whitman College: David Guichard's "Calculus, Chapter 3: Rules for Finding Derivatives, Exercises 3.5, Problems 1-20, 36-39"
Unit 4 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.1: Trigonometric Functions"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.1: Problems 1-4, 11"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.2: The Derivative of sin x"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.3: A Hard Limit"
Whitman College: David Guichard's Calculus: "Chapter 4: Transcendental Functions, Exercises 4.3: Problems 1-7"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.4: The Derivative of sin x, Continued"
Whitman College: David Guichard's Calculus: "Chapter 4: Transcendental Functions, Exercises 4.4: Problems 1-5"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.5: Derivatives of the Trigonometric Functions"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.5: Problems 1-18"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.6: Exponential and Logarithmic Functions"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.7: Derivatives of the Exponential and Logarithmic Functions"
Massachusetts Institute of Technology: David Jerison's "Exponential and Log"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.7: Problems 1-15, 20"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.8: Implicit Differentiation"
Massachusetts Institute of Technology: David Jerison's "Implicit Differentiation"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.8: Problems 1-9, 11-16"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.9: Inverse Trigonometric Functions"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.9: Problems 3-11"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.10: Limits Revisited"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Exercises 4.10: Problems 1-10, 21-24"
Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.11: Hyperbolic Functions"
Unit 5 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Section 5.1: Maxima and Minima"
Massachusetts Institute of Technology: David Jerison's "Curve Sketching"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Exercises 5.1: Problems 1-12, 15"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Section 5.2: The First Derivative Test"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Exercises 5.2: Problems 1-15"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Section 5.3: The Second Derivative Test"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Exercises 5.3: Problems 1-10"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Section 5.4: Concavity and Inflection Points"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Exercises 5.4: Problems 1-9, 19"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Section 5.5: Asymptotes and Other Things to Look For"
Massachusetts Institute of Technology: David Jerison's "Max-Min"
Whitman College: David Guichard's "Calculus, Chapter 5: Curve Sketching, Exercises 5.5, Problems 1-5, 15-19"
Unit 6 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.1: Optimization"
Massachusetts Institute of Technology: David Jerison's "Related Rates"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.1: Problems 5, 7, 9, 10, 14, 16, 22, 26, 28, 33"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.2: Related Rates"
Massachusetts Institute of Technology: David Jerison's "Newton's Method"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.2: Problems 1, 3, 5, 11, 14, 16, 19, 20, 21, 25"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.3: Newton's Method"
Massachusetts Institute of Technology: David Jerison's "The Mean Value Theorem"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.3: Problems 1-4"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.4: Linear Approximations"
Massachusetts Institute of Technology: David Jerison's "Linear and Quadratic Approximations"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Exercises 6.4: Problems 1-4"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative, Section 6.5: The Mean Value Theorem"
Massachusetts Institute of Technology: David Jerison's "The Mean Value Theorem"
Whitman College: David Guichard's "Calculus, Chapter 6: Applications of the Derivative": "Exercises 6.5, Problems 1, 2, 6-9"
Unit 7 Learning Outcomes
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Section 7.1: Two Examples"
Massachusetts Institute of Technology: David Jerison's "Lecture 18: Definite Integrals"
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Exercises 7.1: Problems 1-8"
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Section 7.2: The Fundamental Theorem of Calculus"
Massachusetts Institute of Technology: David Jerison's "The First Fundamental Theorem" and "The Second Fundamental Theorem"
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Exercises 7.2: Problems 7-22"
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Section 7.3: Some Properties of Integrals"
Massachusetts Institute of Technology: David Jerison's "Antiderivatives"
Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Exercises 7.3: Problems 1-6"
Whitman College: David Guichard's "Calculus, Chapter 8: Techniques of Integration, Section 8.1: Substitution"
Massachusetts Institute of Technology: David Jerison's "Antiderivatives"
Whitman College: David Guichard's "Calculus, Chapter 8: Techniques of Integration, Exercises 8.1: Problems 5-19"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 8: Exponential and Logarithmic Functions, Section 8.3: Derivatives of Exponential Functions and the Number e"
University of California, Davis: Duane Kouba's "The Integration of Exponential Functions: Problems 1-12"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 8: Exponential and Logarithmic Functions, Section 8.3: Derivatives of Exponential Functions and the Number e"
University of Houston: Dr. Selwyn Hollis's "Video Calculus: The Natural Logarithmic Function" and "The Exponential Function"
Temple University: Gerardo Mendoza's and Dan Reich's "Calculus on the Web"
Donny Lee's "Hyperbolic Functions" and "Hyperbolic Functions - Derivatives"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 8: Exponential and Logarithmic Functions, Section 8.4: Some Uses of Exponential Functions"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus II: Hyperbolic Functions"
Unit 8 Learning Outcomes
Massachusetts Institute of Technology: David Jerison's "Applications of Logarithms and Geometry"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
Indiana University Southeast: Margaret Ehringe's "Section 5.3 Area between Two Curves"
University of Houston: Dr. Selwyn Hollis's "Video Calculus: Volumes I"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Finding Volumes by Slicing"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.2: Volumes of Solids of Revolution"
Massachusetts Institute of Technology: David Jerison's "Lecture 22: Volumes by Disks and Shells"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
University of Wisconsin H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.3: Length of a Curve"
Massachusetts Institute of Technology: David Jerison's "Parametric Equations, Arclength, Surface Area"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.4: Area of a Surface of Revolution"
Massachusetts Institute of Technology: David Jerison's "Parametric Equations, Arclength, Surface Area"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus II: Areas of Surfaces of Revolution"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.5: Averages"
Massachusetts Institute of Technology: David Jerison's "Work, Average Value, Probability"
Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web"
Whitman College: David Guichard's "Calculus, Chapter 9: Applications of Integration, Section 9.2: Distance, Velocity, Acceleration"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Displacement vs. Distance Traveled"
University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.6: Some Applications to Physics"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Moments and Centers of Mass"
Whitman College: David Guichard's "Calculus, Chapter 9: Applications of Integration, Section 9.5: Work"
Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Work, Fluid Pressures, and Forces"
MA101: Final Exam
Massachusetts Institute of Technology: David Jerison's "Applications of Logarithms and Geometry" ►
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MA101: Single-Variable Calculus I
Sections
Course Introduction
Unit 1: Analytic Geometry
Unit 2: Instantaneous Rate of Change: The Derivative
Unit 3: Rules for Finding Derivatives
Unit 4: Transcendental Functions
Unit 5: Curve Sketching
Unit 6: Applications of the Derivative
Unit 7: Integration
Unit 8: Applications of Integration
Final Exam
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