Calc AB · U6
Integration and Accumulation of Change
Accumulation, Riemann sums, definite integrals, the Fundamental Theorem of Calculus, antiderivatives, substitution, algebraic integration, and technique selection.
Test yourself
A focused, distraction-free run through 55 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 6.1
Exploring Accumulations of Change
Understanding definite integrals as geometric and signed area
Topic 6.2
Approximating Areas with Riemann Sums
Using left, right, midpoint, and trapezoidal approximations
Topic 6.3
Riemann Sums, Summation Notation, and Definite Integral Notation
Connecting finite sums, limits of sums, and definite integrals
Topic 6.4
The Fundamental Theorem of Calculus and Accumulation Functions
Differentiating accumulation functions with variable limits
Topic 6.5
Interpreting the Behavior of Accumulation Functions Involving Area
Using the graph of an integrand to analyze an accumulation function
Topic 6.6
Applying Properties of Definite Integrals
Using additivity, reversal, linearity, symmetry, and average value
Topic 6.7
The Fundamental Theorem of Calculus and Definite Integrals
Evaluating definite integrals using antiderivatives and total change
Topic 6.8
Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
Finding general antiderivatives and particular solutions
Topic 6.9
Integrating Using Substitution
Recognizing composite structure and transforming integrals consistently
Topic 6.10
Integrating Functions Using Long Division and Completing the Square
Rewriting rational functions before applying antiderivative rules
Topic 6.11
Selecting Techniques for Antidifferentiation
Choosing among substitution, algebraic rewriting, completing the square, and basic antiderivative forms