The average temperature in the box

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Homework Help Overview

The discussion revolves around calculating the average temperature in a box using the temperature function T(x,y,z) = 128e^{-x-y-z}. Participants are exploring the integration process and the reasoning behind dividing by a specific value to find the average.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand their integration process and why a division by 4 was used in a similar textbook example. Some participants question the volume calculation of the box and its implications for the average temperature calculation.

Discussion Status

Participants are actively engaging with the problem, with one providing clarification on the average value formula and another questioning the volume calculation. There is no explicit consensus yet, but guidance on the integration and average value concept has been offered.

Contextual Notes

There is a mention of a similar problem in the textbook, which may influence the understanding of the current problem. The volume of the box is under discussion, with differing opinions on its calculation.

whynot314
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Homework Statement


Im not really sure were I am going wrong in the problem there was a similar one in the textbook examples with a different temperature function and they just divided by 4. I really don' t know how my integration is wrong either please help the function if you can't read it is. T(x,y,z)= 128e^{-x-y-z}

[PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0108_zps19442d3b.jpg[/PLAIN]

Homework Equations





The Attempt at a Solution

 
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Your integration is fine, but you seem not to have understood why the other case divided by 4 at the end. The average value of some quantity f(x,y,z) over a region V is ∫f.dv/∫dv, right?
 
To be honest, I did not know. The region in the example was also a box.
 
whynot314 said:
To be honest, I did not know. The region in the example was also a box.

The volume of the box in this case is log(2)*log(4)*log(8), yes? Not 4.
 
yes, thank you.
 

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