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# Unit: Integrals

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## Summation notation review

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Summation notationGet 3 of 4 questions to level up!

## Defining integrals with Riemann sums

#### Quiz 1

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## Interpreting the behavior of accumulation functions

#### Quiz 2

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## Fundamental theorem of calculus and definite integrals

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Antiderivatives and indefinite integralsGet 3 of 4 questions to level up!

## Reverse power rule

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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!

#### Quiz 3

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## Indefinite integrals of common functions

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Indefinite integrals: eˣ & 1/xGet 3 of 4 questions to level up!
Indefinite integrals: sin & cosGet 3 of 4 questions to level up!
Integrating trig functionsGet 5 of 7 questions to level up!

## Definite integrals of common functions

#### Quiz 4

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## Integrating using long division and completing the square

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Integration using long divisionGet 3 of 4 questions to level up!
Integration using completing the squareGet 3 of 4 questions to level up!

## Integrating using trigonometric identities

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Integration using trigonometric identitiesGet 3 of 4 questions to level up!

#### Quiz 5

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## Integrating using linear partial fractions

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Integration with partial fractionsGet 3 of 4 questions to level up!

## Improper integrals

#### Quiz 6

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## Proof 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.