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Lectures 28 and 29 Triple Integrals in Cartesian and Cylindrical Coordinates Calculus II Topic 4: Multiple Integrals

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Building Triple Riemann Integral (1): Making a Partition of a Solid

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Building Triple Riemann Integral (2): Making a Riemann Sum

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Building Triple Riemann Integral (3): Taking the Limit

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Calculating Triple Integrals

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Calculating Triple Integrals (Fubini’s Theorem)

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Calculating Triple Integrals (Fubini’s Theorem)

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Fubini’s Theorem

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Volume and Average Value

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Simple Example

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Volume of a Sphere

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Volume of a Witch Pot as Double and Triple Integral

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Volume of a Wedge

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Volume of a Wedge

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The Volume of something as an Ice Cream

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More Paraboloids

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Changing Order of Integration

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Changing Order of Integration

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More Tetrahedron

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Changing Order of Integration

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Rememberign Cylindrical Coordinates

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Typical Application

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Typical Applications

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Constant Coordinates and Volume Element in Cylindrical Coordinates

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Fubini’s Theorem in Cylindrical Coordinates

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Change of Variables: Cartesian to Cylindrical

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Examples

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Internal Energy of a Salt in a Tank with knownTemperature Distribution

đ?‘‡ đ?‘Ľ, đ?‘Ś, đ?‘§ = 1 + đ?‘Ľ 2 + đ?‘Ś 2 đ?‘…đ?‘Žđ?‘‘đ?‘–đ?‘˘đ?‘ = 2 2 and đ?‘§ ∈ −1,2

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Mass of a Storage of Porous Packed Material đ?œŒ đ?‘Ľ, đ?‘Ś, đ?‘§ = 5 − đ?‘§

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Volume of a Peg-Top

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Homework

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4.6_4.7_Integral_Triple_Cartesianas_Cilindricas  

Calculus II Topic 4: Multiple Integrals Calculus II Santiago de Vicente 1 Santiago de Vicente 2 Calculus II Santiago de Vicente 3 Calculus I...

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