Calc AB · U8
Applications of Integration
Average value, motion and accumulation in context, area between curves, cross-section volumes, and disk/washer volumes about coordinate and shifted axes.
Test yourself
A focused, distraction-free run through 60 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 8.1
Finding the Average Value of a Function on an Interval
Using definite integrals to find and interpret average value
Topic 8.2
Connecting Position, Velocity, and Acceleration Using Integrals
Recovering change in position and velocity from rates
Topic 8.3
Using Accumulation Functions and Definite Integrals in Context
Interpreting integrals as net change in applied settings
Topic 8.4
Finding Area Between Curves Expressed as Functions of x
Using vertical slices and top-minus-bottom integrals
Topic 8.5
Finding Area Between Curves Expressed as Functions of y
Using horizontal slices and right-minus-left integrals
Topic 8.6
Finding Area Between Curves That Intersect at More Than Two Points
Splitting intervals when curve order changes
Topic 8.7
Volumes with Cross Sections: Squares and Rectangles
Building volume integrals from cross-section area formulas
Topic 8.8
Volumes with Cross Sections: Triangles and Semicircles
Using non-rectangular cross-section area formulas
Topic 8.9
Volume with the Disk Method: Revolving Around the x- or y-Axis
Using disks when the region touches the axis of rotation
Topic 8.10
Volume with the Disk Method: Revolving Around Other Axes
Measuring disk radii from non-coordinate axes
Topic 8.11
Volume with the Washer Method: Revolving Around the x- or y-Axis
Using outer-radius squared minus inner-radius squared
Topic 8.12
Volume with the Washer Method: Revolving Around Other Axes
Measuring outer and inner radii from shifted axes