Lectures 28 and 29 Triple Integrals in Cartesian and Cylindrical Coordinates Calculus II Topic 4: Multiple Integrals
Calculus II
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Building Triple Riemann Integral (1): Making a Partition of a Solid
Calculus II
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Building Triple Riemann Integral (2): Making a Riemann Sum
Calculus II
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Building Triple Riemann Integral (3): Taking the Limit
Calculus II
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Calculating Triple Integrals
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Calculating Triple Integrals (Fubini’s Theorem)
Calculus II
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Calculating Triple Integrals (Fubini’s Theorem)
Calculus II
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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
Calculus II
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Change of Variables: Cartesian to Cylindrical
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Examples
Calculus II
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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
Calculus II
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Mass of a Storage of Porous Packed Material đ?œŒ đ?‘Ľ, đ?‘Ś, đ?‘§ = 5 − đ?‘§
Calculus II
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Volume of a Peg-Top
Calculus II
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Homework
Calculus II
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