Triple integrals, changing the order of integration

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Homework Help Overview

The discussion revolves around writing out the triple integral for the volume of a solid defined by specific planes, with a focus on exploring all six possible orders of integration. The subject area is multivariable calculus, specifically dealing with triple integrals.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to identify and describe the different orders of integration for the given solid. There is a request for clarification on how to properly format and present these orders, as well as a focus on the limits of integration.

Discussion Status

Some participants have provided examples of how to describe the integration orders and limits, while others are still working on articulating their findings. There is an ongoing exploration of the various possible orders without reaching a consensus on the final presentation.

Contextual Notes

Participants are encouraged to use LaTeX for clarity in their mathematical expressions. There is an emphasis on not performing the actual integration but rather focusing on the setup of the integrals.

amalone
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Homework Statement



Write out the triple integral for the volume of the solid shown in all six possible orders. Evaluate at least 2 of these integrals.


Homework Equations



I attached a picture of the figure. The front : x/2+z/5=1
right : y/4+z/5=1

The Attempt at a Solution



I really need help with the possible orders and not the actual integration.
I figured out two different orders but I'm not sure how to post them properly
 

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amalone said:

Homework Statement



Write out the triple integral for the volume of the solid shown in all six possible orders. Evaluate at least 2 of these integrals.

Homework Equations



I attached a picture of the figure. The front : x/2+z/5=1
right : y/4+z/5=1

The Attempt at a Solution



I really need help with the possible orders and not the actual integration.
I figured out two different orders but I'm not sure how to post them properly
Hello amalone. Welcome to PF !

attachment.php?attachmentid=55246&d=1359687598.jpg


You can simply describe the order in which you do the integrations, along with the limits of integration.

For example:
(From inner to outer)
Integrate over x from x = 0 to x = 1 - 2z/5 .

Integrate over y from y = 0 to y = 1 - 4z/5 .

Integrate over z from z = 0 to z = 5 .​

You could learn LaTeX and write:

[itex]\displaystyle \int_{0}^{5} \int_{0}^{1 - 4z/5} \int_{0}^{1 - 2z/5\,} dx\,dy\,dz[/itex]
 
SammyS said:
Hello amalone. Welcome to PF !

attachment.php?attachmentid=55246&d=1359687598.jpg


You can simply describe the order in which you do the integrations, along with the limits of integration.

For example:
(From inner to outer)
Integrate over x from x = 0 to x = 1 - 2z/5 .

Integrate over y from y = 0 to y = 1 - 4z/5 .

Integrate over z from z = 0 to z = 5 .​

You could learn LaTeX and write:

[itex]\displaystyle \int_{0}^{5} \int_{0}^{1 - 4z/5} \int_{0}^{1 - 2z/5\,} dx\,dy\,dz[/itex]

Thanks!
 
How about describing the orders of integration that you've found ?
 

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