AP Calculus AB Integration and Accumulation — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 11 definitions and 11 theorems, 7 worked examples, 6 diagrams, in 20 printable pages. This page lists what the notes cover. The notes themselves come with the AP Calculus AB bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Integration and Accumulation — what the notes cover
11 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.
1. Accumulating change \hfill \normalsize\mdseries\itshape topic 6.1
- Definition — Accumulation of change
- Definition — Signed area
Also in this section: 1 worked example, 1 diagram.
2. Riemann sums \hfill \normalsize\mdseries\itshape topic 6.2
- Definition — Riemann sum
- Definition — Trapezoidal sum
- Theorem — Direction of a Riemann or trapezoidal estimate
Also in this section: 1 worked example, 2 diagrams.
3. From a sum to an integral \hfill \normalsize\mdseries\itshape topic 6.3
- Definition — The definite integral
Also in this section: 1 diagram.
4. Properties of the definite integral \hfill \normalsize\mdseries\itshape topic 6.6
- Theorem — Properties of the definite integral
- Definition — Total area and the definite integral
5. Antiderivatives and indefinite integrals \hfill \normalsize\mdseries\itshape topic 6.8
- Definition — Antiderivative
- Definition — Indefinite integral
- Theorem — The basic antiderivatives
Also in this section: 1 note on method and common errors.
6. The Fundamental Theorem: evaluating \hfill \normalsize\mdseries\itshape topic 6.7
- Theorem — The Fundamental Theorem of Calculus: evaluating a definite integral
- Theorem — Net change
Also in this section: 1 worked example.
7. The Fundamental Theorem: accumulation functions \hfill \normalsize\mdseries\itshape topic 6.4
- Definition — The variable of integration
- Definition — Accumulation function
- Theorem — The Fundamental Theorem of Calculus: differentiating an accumulation function
- Theorem — Accumulation with a variable limit that is not
Also in this section: 1 worked example, 1 diagram.
8. Reading an accumulation function off a graph of $f$ \hfill \normalsize\mdseries\itshape topic 6.5
- Theorem — The behaviour of an accumulation function read from the graph of
Also in this section: 1 worked example, 1 diagram.
9. Substitution \hfill \normalsize\mdseries\itshape topic 6.9
- Theorem — Substitution
- Theorem — Substitution in a definite integral
Also in this section: 1 worked example.
10. Long division and completing the square \hfill \normalsize\mdseries\itshape topic 6.10
- Definition — Proper and improper rational expressions
- Theorem — The arctangent form of an antiderivative
Also in this section: 1 worked example.
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 Integration and Accumulation practice worksheet is free and stays free.
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.
- 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
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.
Integration and Accumulation practice worksheet About the Integration and Accumulation unit test