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Avon High School

Avon High School

We Are Avon. We Are One.

Important Links
  • Avon High School
  • AP Calculus AB ACE

Record, Anthony

  • Teacher Profile
  • AP Calculus AB ACE
    • Announcements
    • Course Description / Information
    • Unit 1: Limits
    • Unit 2: Derivatives
    • Unit 3: Straight Line Motion / Implicit Differentiation / Related Rates
    • Unit 4: Extrema and Concavity
    • Unit 5: Limits at Infinity-II & Asymptotes / Curve Sketching & Function Analysis / Optimization
    • Unit 6: Area, Riemann Sums
    • Unit 7: Antidifferentiation, Fundamental Theorems of Calculus & Integration by U-Substitution
    • Unit 8: Transcendental Functions
    • Unit 9: Inverse Trigonometric Functions
    • Unit 10: Slope Fields / Euler's Method / Differential Equations
    • Unit 11: Area Between Curves / Volume of Solids
    • Final Exam Information
    • AP Exam Review Material
    • Continental Math League Material
    • Calculus Lab Information
    • 2016 Summer Packet Information
  • AP Calculus BC ACE
    • Course Description / Information
    • Announcements
    • Unit 12: Applications of Integration - Part II
    • Unit 13: Integration Techniques
    • Unit 14: Partial Fractions, L'Hopital's Rule, Improper Integrals
    • Unit 15: Conics, Parametric Equations and Polar Coordinates
    • Unit 16: Vectors
    • Unit 17: Sequences and Series
    • Unit 18: Power Series, Taylor and Maclaurin Series
    • Continental Math League Material
    • AP Exam Review Material
    • Final Exam Information
  • ACE College Algebra II
    • Course Description / Information
    • Announcements
    • Chapter P: Prerequisites: Fundamental Concepts of Algebra
    • Chapter 1: Equations and Inequalities
    • Chapter 2: Functions and Graphs
    • Chapter 3: Polynomial and Rational Functions
    • Chapter 4: Exponential and Logarithmic Functions
    • Chapter 8: Systems of Equations and Inequalities
    • Chapter 9: Matrices and Determinants
    • Chapter 10: Conic Sections and Analytic Geometry
    • Chapter 11: Sequences, Induction, and Probability
    • Chapter 12: Statistics
    • Final Exam Information
  • S.A.T. Math Prep
  • SRT Class
  • Mr. Record's Schoology Page
  • Note to Teachers and Students outside of Avon High School
  •  
    Unit 7 - Antidifferentiation, Fundamental Theorems of Calculus
                    Integration by u-Substitution 

    Lecture Notes

    Keyed Notes

     
    Section 4.1: Antiderivatives 
     
    Section 4.4: Fundamental Theorems of Calculus 

    Section 4.5: Integration by U-Substitution 
     
     
    4.1 - Antiderivatives - KEYED NOTES 
     
    4.4 - Fundamental Theorems of Calculus - KEYED NOTES 
     
    4.5 - Integration by U-Substitution - KEYED NOTES
     

    Videos/Screencasts

    HW Solutions


     
    Videos on Basic Antidifferentiation
     
    Videos on the Definite Integral 
     
    Videos on the Fundamental Theorem of Calculus 
     
    Videos on Integration by U-Substitution
     
     
    The videos below cover content not tested on the AP Calculus Exam but may be part of a college Calculus I course. 
     
    More Videos on Approximate Integration - Trapezoid Rule and Error Analysis
     
    Videos on Approximation Integration - Simpson's Rule
     
    Videos on Approximate Integration - Simpson's Rule and Error Analysis
     
     
    The following files are solutions to randomly-selected odd exercises that you may find useful when working out your assigned textbook homework problems.
     
    HW 4.1 Solutions 
     
    HW 4.4 - Solutions 
     
    HW 4.5 Solutions
     
     
     
    Unit 7 Exam  Review Files
     
    Unit 7 Review Packet (Sections 4,1, 4.4, 4.5) 
     
    Unit 7 Review (4.1, 4.4, 4.5) - SOLUTIONS

    Homework Worksheets

    Enrichment Activities

    HW 4.1 - Indefinite Integration

    HW 4.4A - The First Fundamental Theorem of Calculus 
     
    HW 4.4B - Average Value of a Function & The Second Fundamental Theorem of Calculus 
     
    HW 4.5A - Integration by U-Substitution 
     
    HW 4.5B - Definite Integration Involving U-Substitution and The Change of Variable Method 


    More Accumulator Function Practice

    Contains Answers

     
Avon High School

Avon High School

We Are Avon. We Are One.

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