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# Integration and accumulation of change

AP Calc: CHA (BI), CHA‑4 (EU), FUN (BI), FUN‑5 (EU), FUN‑6 (EU), LIM (BI), LIM‑5 (EU)

## Exploring accumulations of change

AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.A (LO), CHA‑4.A.1 (EK), CHA‑4.A.2 (EK), CHA‑4.A.3 (EK), CHA‑4.A.4 (EK)

## Approximating areas with Riemann sums

AP Calc: LIM (BI), LIM‑5 (EU), LIM‑5.A (LO), LIM‑5.A.1 (EK), LIM‑5.A.2 (EK), LIM‑5.A.3 (EK), LIM‑5.A.4 (EK)

## Riemann sums, summation notation, and definite integral notation

AP Calc: LIM (BI), LIM‑5 (EU), LIM‑5.B (LO), LIM‑5.B.1 (EK), LIM‑5.B.2 (EK), LIM‑5.C (LO), LIM‑5.C.1 (EK), LIM‑5.C.2 (EK)

#### Quiz 1

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## The fundamental theorem of calculus and accumulation functions

AP Calc: FUN (BI), FUN‑5 (EU), FUN‑5.A (LO), FUN‑5.A.1 (EK), FUN‑5.A.2 (EK)

## Interpreting the behavior of accumulation functions involving area

AP Calc: FUN (BI), FUN‑5 (EU), FUN‑5.A (LO), FUN‑5.A.3 (EK)

#### Quiz 2

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## The fundamental theorem of calculus and definite integrals

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.B (LO), FUN‑6.B.1 (EK), FUN‑6.B.2 (EK), FUN‑6.B.3 (EK)
Practice
Antiderivatives and indefinite integralsGet 3 of 4 questions to level up!

#### Quiz 3

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## Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.C (LO), FUN‑6.C.1 (EK), FUN‑6.C.2 (EK)
Practice
Reverse power ruleGet 3 of 4 questions to level up!
Reverse power rule: sums & multiplesGet 3 of 4 questions to level up!
Reverse power rule: rewriting before integratingGet 3 of 4 questions to level up!

## Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.C (LO), FUN‑6.C.1 (EK), FUN‑6.C.2 (EK)
Practice
Indefinite integrals: eˣ & 1/xGet 3 of 4 questions to level up!
Indefinite integrals: sin & cosGet 3 of 4 questions to level up!

## Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.B (LO), FUN‑6.C (LO)

#### Quiz 4

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## Integrating using substitution

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.C.3 (EK), FUN‑6.D (LO), FUN‑6.D.1 (EK)

## Integrating functions using long division and completing the square

AP Calc: FUN (BI), FUN‑6 (EU), FUN‑6.D (LO), FUN‑6.D.3 (EK)
Practice
Integration using long divisionGet 3 of 4 questions to level up!
Integration using completing the squareGet 3 of 4 questions to level up!

#### Quiz 5

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## Optional videos

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#### Unit test

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### About this unit

The definite integral of a function gives us the area under the curve of that function. Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.
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