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Marlow Works

AP Calculus AB / Unit 8

Unit 8 · 10–15%

Applications of Integration

Integrals find net change, average value, area between curves, and some volumes.

Start first lessonUnit practice

Topics

  • Net change and average value
  • Area between curves
  • Volumes by disks and washers
  • Volumes with known cross sections

Lessons

Key terms

Original practice

Marlow Works questions. If this unit does not have its own items yet, you will see other questions from the same course.

1 of 3Limits and Continuity · easy · multiple choice

What is lim (x→3) of (x² − 9) / (x − 3)?

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Review checklist

  1. 01Sketch the region and name the variable of integration.
  2. 02Find intersection points before you write limits.
  3. 03State the volume method (disk, washer, or slice) in words.

Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

  • Official / link only

    AP Calculus AB course page

    Official eight-unit framework and 2027 exam updates.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

  • Reference only — do not copy

    OpenStax College Algebra 2e

    Algebra reference; current terms include noncommercial and AI-ingestion limits.

    OpenStax · Restricted — see publisher page · accessed 2026-10-01

    Open source