# 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

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

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 Modules: Extrema by the College Board (pdf - 24 pages)

• Practice Problems

• Given the graph of f ' and use FTC to evaluate a value of f

6) Motion: Review Flashcards for motion

7) Net Change Word Problems

• Explanation:

• Practice Problems:

8) Fundamental Theorem of Calculus Review

9) Cumulative Review