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Unit: Integrating multivariable functions

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Line integrals for scalar functions

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Line integrals of scalar functionsGet 3 of 4 questions to level up!

Line integrals for scalar functions (articles)

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Line integrals in vector fields

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Line integrals in vector fieldsGet 3 of 4 questions to level up!
Line integrals in conservative vector fieldsGet 3 of 4 questions to level up!
Distinguishing conservative vector fieldsGet 3 of 4 questions to level up!
Potential functionsGet 3 of 4 questions to level up!

Line integrals in vector fields (articles)

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Quiz 1

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Double integrals

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Iterated integralsGet 3 of 4 questions to level up!
Double integrals with variable boundsGet 3 of 4 questions to level up!
Finding bounds of regionsGet 3 of 4 questions to level up!
Switching bounds on double integralsGet 3 of 4 questions to level up!

Double integrals (articles)

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Quiz 2

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Triple integrals

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Triple integralsGet 3 of 4 questions to level up!

Change of variables

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Change of variables: BoundGet 3 of 4 questions to level up!
Change of variables: FactorGet 3 of 4 questions to level up!

Quiz 3

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Polar, spherical, and cylindrical coordinates

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Double integrals in polarGet 3 of 4 questions to level up!
Integrals in spherical and cylindrical coordinatesGet 3 of 4 questions to level up!

Surface integral preliminaries

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Surface integrals

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Find area elementsGet 3 of 4 questions to level up!
Surface integrals to find surface areaGet 3 of 4 questions to level up!

Surface integrals (articles)

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Quiz 4

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Flux in 3D

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Flux in 3D (articles)

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Unit test

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About this unit

There are many ways to extend the idea of integration to multiple dimensions: Line integrals, double integrals, triple integrals, surface integrals, etc. Each one lets you add infinitely many infinitely small values, where those values might come from points on a curve, points in an area, points on a surface, etc. These are all very powerful tools, relevant to almost all real-world applications of calculus. In particular, they are an invaluable tool in physics.