Integral Functions

Fundamental Theorem of Calculus

Special Focus: by the College Board (pdf - 129 pages) - explains the FTC and includes previous AP questions
Curriculum Module: by the College Board (pdf - 27 pages) - includes lesson plans with solutions and teacher notes

This unit basically defines integral functions and then we take the derivative of integral functions (with their applications). What allows us to take the derivative of integral functions is the Fundamental Theorem of Calculus (the antiderivative part).

Functions defined by integrals

Curriculum Module: Functions defined by Integrals - by the College Board (pdf - 19 pages) - includes handouts and worksheets

1) Definition of Integral Functions

Explanation
- Notes | Annotated
- Interactive website

2) Derivative of Integral Functions

Explanation
- Notes | Annotated
Practice Problems:
- Derivative of Integral Functions WS | Answer

3) Application of the Derivative of Integral Functions (Given an Explicit Integral Function Equation

Explanation:
- Notes | Annotated
Practice Problems:

4) Application of the Derivative Integral Functions Given the Graph of the Integrand

Explanation:
- Notes | Annotated
Practice Problems - Given an integral function and the graph of the integrand
- 2012 Q3
- 2011 Q4; Khan video: part a | part b | part c | part d
- 2009 (Form B) Q3 - part D
- 2005 (Form B) Q4
- 2004 Q5
- 2003 (Form B) Q5
- 2002 Q4
- 2002 (Form B) Q4
- 1999 Q5

5) Net change from a known value (find the value of a function given the derivative of the function and a particular solution):

Explanation:
- Notes | Annotated
- Curriculum Modules: Extrema by the College Board (pdf - 24 pages)
Practice Problems
- Worksheet | Answers
- Given the graph of f ' and use FTC to evaluate a value of f

6) Motion: Review Flashcards for motion

Explanation:
- Notes | Annotated
- Curriculum Module by the College Board (pdf - 30 pages)
- Practice Problems:
  - Motion and Integrals WS | Answers
- Mixed Review Review WS | Answers
- AP Questions (remember on questions #1-3 calculators are allowed; on questions #4-6, no calculators are allowed):
  - 2011 Q1 - Given v(t) explicitly: Khan video: part a | part b, c, and d
    - 2010 (Form B) Q1 - Given v(t) as a graph
  - 2009 (Form B) Q6 - Given v(t) as a table
  - 2009 Q1 - Given v(t) as a table & equation
  - 2008 (Form B) Q3 - Given v(t) as a graph
  - 2008 Q1 - Given v(t) as a graph
  - 2007 (Form B) Q2 - Given v(t) as a graph & equation
  - 2006 (Form B) Q6 - Given v(t) and a(t) as a table
  - 2006 Q4 - Given v(t) as a table
  - 2005 (Form B) Q3 - Given v(t) as an equation
  - 2005 Q5 - Given v(t) as a graph
  - 2004 (Form B) Q3 - Given v(t) as a graph & equation
  - 2004 Q3 - Given v(t) as an equation
  - 2003 (Form B) Q4 -Given v(t) as an equation
  - 2003 Q2 - Given v(t) as an equation
  - 2002 (Form B) Q3 - Given v(t) as an equation
  - 2002 Q3 - Given v(t) as an equation
  - 2001 Q3 - Given a(t) as an equation
  - 2000 Q2 - Given v(t) as a graph and as an equation
  - 1999 Q1 - Given v(t) as an equation
  - 1998 Q3 - Given v(t) as an equation and as a table

7) Net Change Word Problems

Explanation:
- Notes | Annotated
Practice Problems:
- Worksheet | Answers
- Net Change Word Problems WS
- AP Questions
  - 2011 Q2
  - 2010 (Form B) Q3
  - 2010 Q3
  - 2010 Q1
  - 2009 (Form B) Q1
  - 2009 Q3
  - 2009 Q2
  - 2008 Q2 - given a table and an explicit equation
  - 2007 Q2
  - 2006 (Form B) Q4
  - 2006 Q2
  - 2005 (Form B) Q2
  - 2005 Q2
  - 2004 (Form B) Q2
  - 2004 Q1
  - 2003 (Form B) Q2
  - 2003 Q2
  - 2002 (Form B) Q2
  - 2002 Q2
  - 2000 Q4

8) FTC: Antiderivative Review WS | Answers

9) FTC antiderivative part Cumulative Review WS | Answers