Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #471 : Triple Integrals

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Example Question #341 : Triple Integration In Cartesian Coordinates

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Example Question #342 : Triple Integration In Cartesian Coordinates

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Example Question #343 : Triple Integration In Cartesian Coordinates

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Example Question #345 : Triple Integration In Cartesian Coordinates

Integrate:

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Correct answer:

Explanation:

To integrate, we work from the inside outward. 

The first integral is

This becomes the integrand of the next outermost integral, which is

This becomes the integrand of the outermost integral, which is

 

Example Question #346 : Triple Integration In Cartesian Coordinates

Evaluate:

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Correct answer:

Explanation:

To integrate, we work from the inside outwards. 

The first integral we perform is

This becomes the integrand for the next integral:

This becomes the integrand for the last integral:

Example Question #347 : Triple Integration In Cartesian Coordinates

Evaluate

 

 

 

 

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Explanation:

 

First notice the order of integration. We start by integrating with respect to , and we treat  and  as constants. 

 

 

 

Expand the integrand and then integrate with respect to  term-by-term: 

 

 

 

 

 

 

 

 

 

Example Question #348 : Triple Integration In Cartesian Coordinates

Evaluate the following integral 

, where 

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Example Question #951 : Calculus 3

Evaluate the following integral 

, where 

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Example Question #1 : Limits

Evaluate:

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Does not exist

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Explanation:

Since we won't have any divided by zero problems, we can just evaluate at the point.

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