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# Applications of integration

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

AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.B (LO), CHA‑4.B.1 (EK)

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Average value over a closed intervalCalculating average value of function over intervalMean value theorem for integrals

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Average value of a functionGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.C (LO), CHA‑4.C.1 (EK)

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Motion problems with integrals: displacement vs. distanceAnalyzing motion problems: positionAnalyzing motion problems: total distance traveledMotion problems (with definite integrals)Worked example: motion problems (with definite integrals)Average acceleration over interval

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Analyzing motion problems (integral calculus)Get 3 of 4 questions to level up!

Motion problems (with integrals)Get 3 of 4 questions to level up!

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

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Area under rate function gives the net changeInterpreting definite integral as net changeWorked examples: interpreting definite integrals in contextAnalyzing problems involving definite integralsAnalyzing problems involving definite integralsWorked example: problem involving definite integral (algebraic)

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Interpreting definite integrals in contextGet 3 of 4 questions to level up!

Analyzing problems involving definite integralsGet 3 of 4 questions to level up!

Problems involving definite integrals (algebraic)Get 3 of 4 questions to level up!

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

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Area between a curve and the x-axisArea between a curve and the x-axis: negative areaArea between curvesWorked example: area between curvesComposite area between curves

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Area between a curve and the x-axisGet 3 of 4 questions to level up!

Area between two curves given end pointsGet 3 of 4 questions to level up!

Area between two curvesGet 3 of 4 questions to level up!

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

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Area between a curve and the 𝘺-axisHorizontal area between curves

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Horizontal areas between curvesGet 3 of 4 questions to level up!

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

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No videos or articles available in this lesson

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Area between curves that intersect at more than two points (calculator-active)Get 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.1 (EK)

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Volume with cross sections: introVolume with cross sections: squares and rectangles (no graph)Volume with cross sections perpendicular to y-axis

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Volumes with cross sections: squares and rectangles (intro)Get 3 of 4 questions to level up!

Volumes with cross sections: squares and rectanglesGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.2 (EK), CHA‑5.B.3 (EK)

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Volume with cross sections: semicircleVolume with cross sections: triangle

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Volumes with cross sections: triangles and semicirclesGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.1 (EK)

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Disc method around x-axisGeneralizing disc method around x-axisDisc method around y-axis

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Disc method: revolving around x- or y-axisGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.2 (EK)

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Disc method rotation around horizontal lineDisc method rotating around vertical lineCalculating integral disc around vertical line

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Disc method: revolving around other axesGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.3 (EK)

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Solid of revolution between two functions (leading up to the washer method)Generalizing the washer method

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Washer method: revolving around x- or y-axisGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.4 (EK)

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Washer method rotating around horizontal line (not x-axis), part 1Washer method rotating around horizontal line (not x-axis), part 2Washer method rotating around vertical line (not y-axis), part 1Washer method rotating around vertical line (not y-axis), part 2

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Washer method: revolving around other axesGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑6 (EU), CHA‑6.A (LO), CHA‑6.A.1 (EK)

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Arc length introWorked example: arc length

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Arc lengthGet 3 of 4 questions to level up!

AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.B (LO), CHA‑4.C (LO), CHA‑4.E (LO)

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No videos or articles available in this lesson

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Contextual and analytical applications of integration (calculator-active)Get 3 of 4 questions to level up!

### About this unit

Definite integrals are all about the accumulation of quantities. Let's see how they are applied in order to solve various kinds of problems.AP® is a registered trademark of the College Board, which has not reviewed this resource.