Basic calculus question

1. Mar 19, 2012

pamparana

Hello everyone,

I have an integral of the following form:

log($\int_{r}^{\inf}\frac{P(r,f)}{P(f)}dr)$

Now, my question is that since the integral is wrt to r, can I bring P(f) outside. So:

$\frac{1}{P(f)}$log($\int_{r}^{\inf}P(r,f)dr)$

Thanks,

Luca

2. Mar 19, 2012

micromass

You can bring it outside the integral.
But you also brought it outside the log, which is wrong.

3. Mar 19, 2012

Robert1986

Outside of the integral? Yes. Outside of the log? no.

4. Mar 19, 2012

HallsofIvy

You can, of course, say
$$ln\left(\frac{1}{P(f)}\int P(r,f)dr\right)= ln\left(\int P(r,f)dr\right)- ln(P(f))$$

By the way, it is not a good idea to use r as the lower limit of the integral and as the variable of integration.

5. Mar 19, 2012

Staff: Mentor

Also, since P(r, f) and P(f) appear to be different functions with different domains, they should have different names.

6. Mar 19, 2012

genericusrnme

It could be that $P(f) \equiv P(r_0 , f)$ for some fixed $r_0$, I've seen that used quite a lot.

7. Mar 19, 2012

pamparana

Thank you guys. That is very helpful. Sorry, did not intend to put it outside the log in my original post! Latex type :)

Many thanks,

Luca