Question

Anyone have an idea how to integrate this definite integral? http://i.imgur.com/PD1oU.jpg

Answer 1

what is \(T_w\) ?

Answer 2

Temperature of water, it's constant.

Answer 3

then it's just a simple u-sub\[u=T-T_w\implies du=dT\]

Answer 4

I have the solution, but I do not how it was integrated : [

Answer 5

\[\int{dT\over T-T_w}\]let\[u=T-T_w\implies du=dT\]the integral is then\[\int\frac{du}u=\ln |u|+C=\ln|T-T_w|+C\](you asked for indefinite)

Answer 6

Thank you, I saw the limits so I automatically assumed it was a definite integral.

Answer 7

what you have is definite
I thought you asked for the indefinite, my mistake
so just evaluate the indefinite