Unit 6: Integration and Accumulation of Change
Duration of Days: 19
Student Outcomes:
Accumulation of Change: Students will understand that the area under a velocity curve represents the total distance traveled.
Riemann Sums: Students will learn to estimate area using rectangles (Left, Right, Midpoint) and Trapezoids.
The Antiderivative: Students will master the "Power Rule in reverse" and understand the necessity of the constant +C.
The Fundamental Theorem of Calculus (FTC): This is the crown jewel of the unit. Students will use it to evaluate definite integrals and understand how a derivative can "cancel out" an integral.
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite
Integral Notation
6.4 The Fundamental Theorem of Calculus and
Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions
Involving Area
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite
Integrals
6.8 Finding Antiderivatives and Indefinite Integrals:
Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division
and Completing the Square
6.14 Selecting Techniques for Antidifferentiation
AP College Board Classroom Assessments