Weird double integral. Please help

[racnna]

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!

 

[chiro]

Hey racnna and welcome to the forums.

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

 

[racnna]

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!

 

[genericusrnme]

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 \int_a^b \partial _x f(x,y) dx = f(b,y)-f(a,y)

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