1. Home
  2. Unit notes
  3. AP Calculus AB
  4. Applications of Integration
AP Calculus AB In the AP Calculus AB bundle

AP Calculus AB Applications of Integration — Unit Notes

Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 11 definitions and 6 theorems, 5 worked examples, 8 diagrams, in 15 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.

Unit notes — in the bundle

15 pages 17 definitions & theorems 5 worked examples 37 key words 6 Try-it pairs, answered 14-row at-a-glance table 37-entry glossary Fill-in-the-blank guided twin 8 diagrams Letter size, print-ready

Not sold separately. The practice worksheet for this unit is free, with no email and no account.

Applications of Integration — what the notes cover

7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.

Also in this section: 2 notes on method and common errors.

What you need

Also in this section: 1 note on method and common errors.

Average value

  • Definition — Average value of a function
  • Theorem — The average value of a rate of change

Also in this section: 1 worked example, 1 diagram.

Motion: displacement and distance

  • Definition — Displacement
  • Definition — Total distance travelled

Also in this section: 1 worked example, 1 diagram.

Accumulation and net change

  • Definition — Accumulation function
  • Theorem — Net change

Area between curves

  • Definition — Area between two curves in x
  • Definition — Area between two curves in y
  • Theorem — Signed area and area

Also in this section: 2 worked examples, 3 diagrams.

Volumes with cross sections

  • Theorem — Volume by cross sections
  • Definition — The cross-sectional segment
  • Definition — Areas of the standard cross sections

Also in this section: 1 diagram.

Volumes of revolution

  • Theorem — The disc method
  • Definition — The direction of a slice
  • Definition — Radius about a shifted axis
  • Theorem — The washer method
  • Definition — Inner radius about a shifted axis

Also in this section: 1 worked example, 1 note on method and common errors, 2 diagrams.

Where the notes are

The notes are one of the documents in the AP Calculus AB Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Applications of Integration practice worksheet is free and stays free.

Best value for the whole year

Every AP Calculus AB topic — the complete Solutions Bundle

One download, one payment, the whole program. For all 8 AP Calculus AB units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.

8 units · 64 PDFs · 527 pages$19.99
  • Worked solutions, not answer lists — every step written out
  • Covers the whole year's program at this level
  • Less than the price of one hour of tutoring — for the entire year's solutions
Everything paid, in one file $19.99CAD · one payment AP Calculus AB bundle — coming soon Not on sale yet

Practise it, then test yourself

Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.

Applications of Integration practice worksheet   About the Applications of Integration unit test

← All 8 AP Calculus AB unit notes

Free practice worksheet

Ready to improve your grades?

WhatsApp is the way to reach me — tell me the course you're taking and what you're stuck on, and we'll sort out a first session from there.

Message Me on WhatsApp

or send a message

I reply within a day, usually sooner. Your details are used only to answer you — see the Privacy Policy.

Private math & science tutoring in Montreal, QC — Westmount · Outremont · Town of Mount Royal · Hampstead · Côte-Saint-Luc · NDG · Nuns' Island · West Island — and online across Quebec.

Chat with Marius