# 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

2009 (Form B) Q3

*- part D*

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

**Explanation:**Curriculum Module by the College Board (pdf - 30 pages)

**Practice Problems:**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 d2010 (Form B) Q1 - Given

*v*(*t*) as a graph2009 (Form B) Q6 - Given

*v*(*t*) as a table2009 Q1 - Given

*v*(*t*) as a table & equation2008 (Form B) Q3 - Given

*v*(*t*) as a graph2008 Q1 - Given

*v*(*t*) as a graph2007 (Form B) Q2 - Given

*v*(*t*) as a graph & equation2006 (Form B) Q6 - Given

*v*(*t*) and*a*(*t*) as a table2006 Q4 - Given

*v*(*t*) as a table2005 (Form B) Q3 - Given

*v*(*t*) as an equation2005 Q5 - Given

*v*(*t*) as a graph2004 (Form B) Q3 - Given

*v*(*t*) as a graph & equation2004 Q3 - Given

*v*(*t*) as an equation2003 (Form B) Q4 -Given

*v*(*t*) as an equation2003 Q2 - Given

*v*(*t*) as an equation2002 (Form B) Q3 - Given

*v*(*t*) as an equation2002 Q3 - Given

*v*(*t*) as an equation2001 Q3 - Given

*a*(*t*) as an equation2000 Q2 - Given

*v*(*t*) as a graph and as an equation1999 Q1 - Given

*v*(*t*) as an equation1998 Q3 - Given

*v*(*t*) as an equation and as a table

**7) Net Change Word Problems**

**Explanation:****Practice Problems:**AP Questions

**8) Fundamental Theorem of Calculus Review**

**9) Cumulative Review**