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Marlow Works

AP Calculus AB / Unit 6

Unit 6 · 15–20%

Integration and Accumulation of Change

An integral adds little bits of a rate and returns net change.

Start first lessonUnit practice

Topics

  • Antiderivatives
  • Riemann sums
  • Definite integrals
  • Fundamental Theorem of Calculus
  • Substitution

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 1Integration and Accumulation of Change · hard · free response

Water enters a tank at a rate r(t) = 8 − 0.5t liters per minute for 0 ≤ t ≤ 10. At t = 0 the tank holds 20 liters. (a) Write an expression for the volume V(t). (b) Find V(6). (c) Interpret V(6) − V(0) in context.

Original Marlow Works item — not a College Board question.

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

Review checklist

  1. 01State whether a Riemann sum is left, right, or midpoint, and whether it over- or underestimates.
  2. 02Keep units: (rate unit) × (input unit) = accumulated unit.
  3. 03When you substitute, change the limits or change back to x.

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