Weird double integral. Please help

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Discussion Overview

The discussion revolves around a double integral encountered in a thermodynamics context, focusing on the mathematical techniques used to transition between two forms of the integral. Participants explore the disappearance of a partial differential and the 'dT' term in the integral transformation.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how a partial differential and 'dT' vanish in the transformation of the integral.
  • Another participant suggests familiarity with identities related to the fundamental theorem of calculus as potentially relevant to the problem.
  • A different participant mentions the evaluation of the 'dt' integral using a specific identity from calculus, referencing the evaluation of a partial derivative integral.
  • A link to a Wikipedia page on differentiation under the integral sign is provided as a potential resource for further understanding.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specific mathematical identity or technique needed to clarify the integral transformation, indicating that the discussion remains unresolved.

Contextual Notes

There may be limitations in the participants' understanding of the fundamental theorem of calculus and its applications, as well as the specific context of the thermodynamics problem.

racnna
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Weird double integral. Please help!

its from thermodynamics...but i don't think you really need to understand thermodynamics to figure out what math trick they used to get from the first integral to the second integral
http://img833.imageshack.us/img833/833/intek.png


i have been looking at this equation for hours and cannotfigure out how that partial differential and the 'dT' just disappeared!
 
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Hey racnna and welcome to the forums.

Are you familiar with identities involving the fundamental theorem of calculus?
 


hey chiro...no I am not..or maybe i have just forgotten...i just googled but can't seem to find any useful info...can you please explain this identity or link me to a place that explains it? thanks!
 


racnna said:
hey chiro...no I am not..or maybe i have just forgotten...i just googled but can't seem to find any useful info...can you please explain this identity or link me to a place that explains it? thanks!

they evaluated the dt integral using the fact that [itex]\int_a^b \partial _x f(x,y) dx = f(b,y)-f(a,y)[/itex]

you might find this helpful;
http://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign
 

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