# Integral Functions

__Fundamental Theorem of Calculus __

**Special Focus:****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

**2) Derivative of Integral Functions**

- Explanation
- Practice Problems:

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

- Explanation:
- Practice Problems:

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

- Explanation:
- 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:
- Practice Problems

**6) Motion: Review Flashcards for motion**

- Explanation:
- Notes | Annotated
- Curriculum Module by the College Board (pdf - 30 pages)
- Practice Problems:
- 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

- 2010 (Form B) Q1 - Given
- 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

- 2011 Q1 - Given

**7) Net Change Word Problems**

- Explanation:
- Practice Problems:
- Worksheet | Answers
- Net Change Word Problems WS
- AP Questions