AP®︎ Calculus BC Unit 6: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 6 of AP Calculus BC – Integration and Accumulation of Change.
Unit 6: Integration and Accumulation of Change
Learn definite integrals, FTC, Riemann sums, antiderivatives, and improper integrals.
Begin with Topic 6.1: Exploring Accumulations o...To review Unit 6, go through each of the 14 topics below.
Everything you actually need to know for your Unit 6 test, pulled directly from the AP® Calculus BC curriculum.
Exploring Accumulations of Change
Exploring Accumulations of Change
- Accumulation of Change from a Rate Function
- Signed Area and What It Means
- Finding Accumulation from a Graph
Approximating Areas with Riemann Sums
Approximating Areas with Riemann Sums
- What a Riemann Sum Is
- The Four Main Approximation Methods
- How to Compute a Riemann Sum
Riemann Sums, Summation Notation, and Definite Integral Notation
Riemann Sums, Summation Notation, and Definite Integral Notation
- What a Riemann Sum Is
- Writing Riemann Sums in Sigma Notation
- The Definite Integral as a Limit
The Fundamental Theorem of Calculus and Accumulation Functions
The Fundamental Theorem of Calculus and Accumulation Functions
- The Fundamental Theorem of Calculus and Accumulation Functions
- What an Accumulation Function Represents
- Representing Accumulation Functions with Integrals
Interpreting the Behavior of Accumulation Functions Involving Area
Interpreting the Behavior of Accumulation Functions Involving Area
- What an Accumulation Function Is
- Analyzing \(g(x) = \int_a^x f(t)\,dt\) from Information About \(f\)
- Working Across Representations
Applying Properties of Definite Integrals
Applying Properties of Definite Integrals
- What a Definite Integral Represents
- The Core Properties of Definite Integrals
- Using Geometry to Evaluate Definite Integrals
The Fundamental Theorem of Calculus and Definite Integrals
The Fundamental Theorem of Calculus and Definite Integrals
- Antiderivatives and What the Fundamental Theorem Connects
- FTC Part 1 and Differentiating Definite Integrals
- FTC Part 2 and Evaluating Definite Integrals
Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- What an Antiderivative and Indefinite Integral Are
- Core Rules for Finding Antiderivatives
- How to Actually Do the Process
Integrating Using Substitution
Integrating Using Substitution
- What Substitution Is and Why It Works
- The Substitution Process
- When Substitution Is the Right Tool
Integrating Functions Using Long Division and Completing the Square
Integrating Functions Using Long Division and Completing the Square
- Rewriting the Integrand So It Matches a Known Antiderivative
- Integrating Rational Functions Using Long Division
- Completing the Square
Integrating Using Integration by Parts
Integrating Using Integration by Parts
- Integration by Parts
- When Integration by Parts Works Best
- The Method Step by Step
Integrating Using Linear Partial Fractions
Integrating Using Linear Partial Fractions
- What linear partial fractions are
- When this method applies
- The decomposition setup
Evaluating Improper Integrals
Evaluating Improper Integrals
- What an Improper Integral Is
- Rewriting as a Limit
- Evaluating Step by Step
Selecting Techniques for Antidifferentiation
Selecting Techniques for Antidifferentiation
- Selecting a Technique for Antidifferentiation
- Core Antiderivative Patterns to Recognize First
- U-Substitution
Notes
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