Calculus 3 : Triple Integration in Cartesian Coordinates

Study concepts, example questions & explanations for Calculus 3

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Example Question #341 : Triple Integration In Cartesian Coordinates

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Correct answer:

Explanation:

Example Question #342 : Triple Integration In Cartesian Coordinates

Possible Answers:

Correct answer:

Explanation:

Example Question #343 : Triple Integration In Cartesian Coordinates

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Correct answer:

Explanation:

Example Question #344 : Triple Integration In Cartesian Coordinates

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Correct answer:

Explanation:

Example Question #473 : Multiple Integration

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 #345 : Triple Integration In Cartesian Coordinates

Evaluate:

Possible Answers:

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 #480 : Triple Integrals

Evaluate

 

 

 

 

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Correct answer:

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 #951 : Calculus 3

Evaluate the following integral 

, where 

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Correct answer:

Explanation:

Example Question #482 : Triple Integrals

Evaluate the following integral 

, where 

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Correct answer:

Explanation:

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