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### Integral Functions

 Fundamental Theorem of Calculus Special Focus: by the College Board (pdf - 129 pages) - explains the FTC and includes previous AP questionsCurriculum Module: by the College Board (pdf - 27 pages) - includes lesson plans with solutions and teacher notesThis 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 integralsCurriculum Module: Functions defined by Integrals - by the College Board (pdf - 19 pages) - includes handouts and worksheets1) Definition of Integral FunctionsExplanation2)  Derivative of Integral FunctionsExplanationNotes | AnnotatedPractice Problems:Derivative of Integral Functions WS | Answer3)  Application of the Derivative of Integral Functions (Given an Explicit Integral Function EquationExplanation:Notes | Annotated Practice Problems:4) Application of the Derivative Integral Functions Given the Graph of the IntegrandExplanation:Notes | AnnotatedPractice Problems - Given an integral function and the graph of the integrand2012 Q32011 Q4; Khan video:2009 (Form B) Q3 - part D2005 (Form B) Q42004 Q52003 (Form B) Q52002 Q42002 (Form B) Q41999 Q55)  Net change from a known value (find the value of a function given the derivative of the function and a particular solution): Explanation:Notes | AnnotatedCurriculum Modules: Extrema by the College Board (pdf - 24 pages) Practice ProblemsWorksheet | AnswersGiven the graph of f ' and use FTC to evaluate a value of f6)  Motion:  Review Flashcards for motionExplanation:Notes | AnnotatedCurriculum Module by the College Board (pdf - 30 pages)Practice Problems:Motion and Integrals WS | AnswersMixed Review Review WS | AnswersAP 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 table7)  Net Change Word ProblemsExplanation:Practice Problems:Worksheet | AnswersNet Change Word Problems WSAP Questions9) FTC antiderivative part Cumulative Review WS | Answers