AP®︎ Calculus AB Unit 8: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 8 of AP Calculus AB – Applications of Integration.
Unit 8: Applications of Integration
Apply integrals to compute areas, volumes, and solve net-change problems.
Begin with Topic 8.1: Finding the Average Value...To review Unit 8, go through each of the 12 topics below.
Everything you actually need to know for your Unit 8 test, pulled directly from the AP® Calculus AB curriculum.
Finding the Average Value of a Function on an Interval
Finding the Average Value of a Function on an Interval
- What the Average Value of a Function Is
- The Formula and What Each Part Means
- How to Find the Average Value
Connecting Position, Velocity, and Acceleration of Functions Using Integrals
Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- Position, Velocity, and Acceleration in Rectilinear Motion
- Displacement vs Total Distance Traveled
- Using Integrals to Move Between a, v, and s
Using Accumulation Functions and Definite Integrals in Applied Contexts
Using Accumulation Functions and Definite Integrals in Applied Contexts
- What an Accumulation Function Represents
- The Net Change Formula in Applied Contexts
- How to Solve Accumulation Problems
Finding the Area Between Curves Expressed as Functions of x
Finding the Area Between Curves Expressed as Functions of x
- Area Between Two Curves as a Definite Integral
- The Full Setup Process
- When the Top Function Changes
Finding the Area Between Curves Expressed as Functions of y
Finding the Area Between Curves Expressed as Functions of y
- What Area Between Curves Using y Means
- Setting Up the Integral with Respect to y
- When Horizontal Slices Are Better
Finding the Area Between Curves That Intersect at More Than Two Points
Finding the Area Between Curves That Intersect at More Than Two Points
- What Area Between Intersecting Curves Means
- Why More Than Two Intersections Changes Things
- The Complete Strategy
Volumes with Cross Sections: Squares and Rectangles
Volumes with Cross Sections: Squares and Rectangles
- Volume from Known Cross Sections
- Types of Cross Sections on the AP Exam
- How to Set Up the Integral
Volumes with Cross Sections: Triangles and Semicircles
Volumes with Cross Sections: Triangles and Semicircles
- How volumes with known cross sections work
- The cross-section shapes you must know
- Setting up the volume step by step
Volume with Disc Method: Revolving Around the x- or y-Axis
Volume with Disc Method: Revolving Around the x- or y-Axis
- What the Disc Method Is
- Revolving Around the x-Axis
- Revolving Around the y-Axis
Volume with Disc Method: Revolving Around Other Axes
Volume with Disc Method: Revolving Around Other Axes
- What the Disc Method Is Really Doing
- Horizontal vs. Vertical Axes
- Visualizing What’s Happening
Volume with Washer Method: Revolving Around the x- or y-Axis
Volume with Washer Method: Revolving Around the x- or y-Axis
- What the Washer Method Is
- Visualizing a Washer
- Revolving Around the x-Axis
Volume with Washer Method: Revolving Around Other Axes
Volume with Washer Method: Revolving Around Other Axes
- What the Washer Method Around Other Axes Is
- Geometry First Then Algebra
- Choosing the Variable
Notes
1 credit used · 5/5 remaining