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  • TOPICS
  • TOPICS 2A - 2H
  • TOPICS 4A - 4E

Second Semester AP Calculus 2019-2020


Topics

  • Approximation of areas under a curve using rectangles
  • Finding the integrals of basic functions
  • Using U-substitution to find integrals of more complex functions
MS Teams Assignments 
  1. Rank and Integrate Using U Substitution
  2. PON 5.3 Problems & Assignment
Goals
  • Be able to use LRAM, RRAM, MRAM to approximate areas under curve
  • Understand the connection to "positive" and "negative" areas and integration
  • Be able to connect derivative to the integration process
  • Be able to use properties of integrals to take integrals of polynomials, rational, radical, exponential, logarithmic functions, or trigonometric functions
  • Be able to use u substitution to find integrals of more complex functions
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Practice 

Integration Basics Practice
  • PON 5.1 HWK​​
  • PON 5.1 ASSIGNMENT​
  • PON 5.2 HWK​
  • PON 5.2 ASSIGNMENT​​
  • PON 5.1 HWK Solutions
  • ​PON 5.1 Assignment
  • ​PON 5.2 HWK Solutions
  • ​PON 5.2 Assignment​
  • KUTA Power rule practice with answers
  • MATH AIDS Power Rule Practice with answers
  • MATH AIDS Power Rule Practice with answers 2

Area under Curve
  • PON 5.5 HWK
  • PON 5.5 ASSIGNMENT
  • ​​PON 5.5 HWK Solutions
  • ​PON 5.5 Assignment
  • KUTA Area under curve using rectangles with answers
  • KUTA Riemann Sum Area for a function based on a table
  • ​KUTA Area under Curve through Definite Integration
    • problems 11-16 require piecewise or u substitution
    • FTC 1
  • KUTA Second Fundamental Theorem of Calculus 

U Substitution
The reverse of the Chain Rule
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  • PON 5.3 HWK
    • ​​PON 5.3 HWK Solutions
  • PON 5.3 Assignment
  • ​PON 5.4 HWK
    • ​​PON 5.4 HWK Solutions​​
  • PON 5.4 Assignment
  • ​KUTA U Substitution
  • KUTA U Substitution​​ 2​
  • U Substitution Practice 
  • U Substitution Practice 2
    • Worked Out ​Solutions
  • ​U Substitution Practice 3
  • U Substitution Practice 4
    • ​​worked out solutions
  • ​​U Substitution Practice 5
    • ​​worked out solutions

Integration of Exponential and Logarithmic Functions
  • KUTA Logarithm and Exponential Integrals
  • KUTA Logarithm and Exponential Integrals 2
  • MATH AIDS Log and Exponential Practice with answers
  • MATH AIDS Log and Exponential Practice with answers 2
  • MATH AIDS Log and Exponential Practice with answers 3

Integration of Trigonometric Functions
  • ​KUTA Trigonometric Function Integrals
  • KUTA Trigonometric Function Integrals 2
  • MATH AIDS Trigonometric Practice with answers
  • MATH AIDS Trigonometric Practice with answers 2

Integration of Inverse Trigonometric Functions 
  • KUTA Inverse Trigonometric Function Integrals
  • ​KUTA Inverse Trigonometric Function Integrals 2
  • MATH AIDS Inverse Trig Function Practice with answers
  • MATH AIDS Inverse Trig Function Practice with answers 2
  • MATH AIDS Inverse Trig Function Practice with answers 3

Mixed Integration Practice
  • Mixed Integration with Answers
  • ​Mixed Integration with Answers 2
  • ​Mixed Integration 3
    • ​​worked out solutions
  • ​​​Mixed Integration 4
    • ​​worked out solutions​
  • ​​Mixed Integration 5
    • ​​worked out solutions​​
  • ​​Mixed Integration 6
    • ​​worked out solutions​
  • ​​​Mixed Integration 7
    • ​​worked out solutions​​

Links and Resources
  • Paul's Online Notes for Calc 1
  • ​A Free Calculus Book
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  • Indefinite Integral Lecture
  • U Substitution Lecture
  • ​Area under curve through Limits Lecture
  • Definite Integral Lecture
  • ​Fundamental Theorem of Calculus Lecture​​
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  • Calculus Directory
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  • Anti-Derivative Lecture
  • Definite Integrals Lecture
  • Fundamental Theorem of Calculus I Lecture 
  • Fundamental Theorem of Calculus II Lecture
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  • Integration Directory
  • Optimization links 
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  • Calculus Directory
  • Integration Directory
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  • Integration Basics 1
  • Integration Basics 2
  • ​Indefinite Integrals 1
  • Fundamental Theorem of Calculus 1
  • FTC 2
  • ​FTC 3
  • ​FTC 4
  • ​FTC 5
  • ​FTC 6
  • ​FTC 7
  • ​U Substitution 1
  • U Substitution 2​
  • ​U Substitution 3
  • U Substitution 4
  • ​U Substitution 5
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  • Calculus Directory

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  • Introduction to Integrals
  • U Substitution
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  • U Substitution​​
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  • LRAM Example
  • ​RRAM Example
  • ​MRAM Example
  • ​Riemann Sum with Rectangles
  • quartic functions
  • ​cubic functions
  • ​quadratic functions
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​Mr Hickman's Resources
  • optimization 2018-2019