Weird double integral. Please help!!

racnna

its from thermodynamics...but i dont 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



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 im not..or maybe i have just forgotten....i just googled but cant seem to find any useful info....can you please explain this identity or link me to a place that explains it? thanks!

genericusrnme

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/Differe..._integral_sign