Exam Strategy

Calculus AB · AP · Applications of Integration

CED focus

Volume with Disc Method: Revolving Around Other Axes

This topic is assessed on the AP Exam.

Multiple-choice tips

• Decide if the item is net change, total area, or volume before integrating.
• Choose washer vs shell vs cross-section from the region description.
• Eliminate volume setups missing π or using wrong thickness variable.
• On motion MC, separate displacement from total distance.
• Check dx vs dy consistency with bounds.

Free-response tips

• State integrand meaning and units; show FTC or Riemann setup explicitly.
• Draw the region and label a representative slice (dx or dy).
• Write the volume or area integral with integrand and bounds before evaluating.
• Show particle motion integrals with correct sign for direction.
• State what the integral represents in one sentence.

Common traps

• Wrong limits or missing π in volume setups
• Mixing dx and dy in the same integral
• Forgetting π in disk/washer volume
• Confusing displacement with total distance traveled

Quick checklist

• [ ] Can set up a volume integral with a labeled diagram
• [ ] Can write displacement vs distance integrals
• [ ] Can explain what the integral measures