AP®︎ Calculus BC Unit 8: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 8 of AP Calculus BC – Applications of Integration.
Unit 8: Applications of Integration
Apply integrals to compute areas, volumes, arc lengths, and solve net-change problems.
Begin with Topic 8.1: Finding the Average Value...To review Unit 8, go through each of the 13 topics below.
Everything you actually need to know for your Unit 8 test, pulled directly from the AP® Calculus BC 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
- How to Find the Average Value
- Why This Shows Up on Tests
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 from Velocity
- Distance Traveled
Using Accumulation Functions and Definite Integrals in Applied Contexts
Using Accumulation Functions and Definite Integrals in Applied Contexts
- Accumulation and Net Change
- Interpreting Definite Integrals in Context
- Solving Accumulation Problems
Finding the Area Between Curves Expressed as Functions of x
Finding the Area Between Curves Expressed as Functions of x
- What the Area Between Two Curves Is
- How to Find the Area Step by Step
- 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
- Horizontal Slices and Integrating with Respect to y
- When You Should Use dy
- Setting Up the Integral Correctly
Finding the Area Between Curves That Intersect at More Than Two Points
Finding the Area Between Curves That Intersect at More Than Two Points
- Area Between Curves That Intersect More Than Twice
- Why One Integral Is Not Enough
- The Complete Strategy
Volumes with Cross Sections: Squares and Rectangles
Volumes with Cross Sections: Squares and Rectangles
- Volume from Known Cross Sections
- The Base Region and Slice Direction
- Square Cross Sections
Volumes with Cross Sections: Triangles and Semicircles
Volumes with Cross Sections: Triangles and Semicircles
- Volumes from known cross sections
- Triangular cross sections
- Semicircular cross sections
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
- The Two Disc Formulas
- How to Set Up a Disc Problem
Volume with Disc Method: Revolving Around Other Axes
Volume with Disc Method: Revolving Around Other Axes
- Disc method around any horizontal or vertical line
- Rotating around a horizontal line \( y = b \)
- Rotating around a vertical line \( x = a \)
Volume with Washer Method: Revolving Around the x- or y-Axis
Volume with Washer Method: Revolving Around the x- or y-Axis
- The Washer Method for Volumes of Revolution
- Outer and Inner Radius
- How to Set Up a Washer Problem
Volume with Washer Method: Revolving Around Other Axes
Volume with Washer Method: Revolving Around Other Axes
- Washer Method Around a Horizontal or Vertical Line
- How to Set Up the Integral Correctly
- Choosing dx or dy
The Arc Length of a Smooth, Planar Curve and Distance Traveled
The Arc Length of a Smooth, Planar Curve and Distance Traveled
- Arc Length of a Smooth Planar Curve
- Determining Length with a Definite Integral
- Distance Traveled
Notes
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