I'm looking for a book/paper/online source where the following formula is shown to be true:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac d{dt} \int_{a(t)}^{b(t)} f(t,\tau)d\tau =\int_{a(t)}^{b(t)} \frac {\partial f(t,\tau)}{\partial t} d\tau\,+\, \frac {da(t)}{dt}f(t,a(t))\,-\, \frac {db(t)}{dt}f(t,b(t))[/tex]

I know one should post attempts at solving the problem but to be honest I wouldn't know where to start. That's one of the reasons why I asked for a reference that would explain/elucidate the proof rather than the proof itself (as well as such a source probably being very useful to me in general). I will say that I can show the Fundamental Theorem of Calculus to be true where the integrand is a function of only one variable if that helps..

Thanks for taking the time to read. Any help you offer will be very much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Advanced calculus

**Physics Forums | Science Articles, Homework Help, Discussion**