Solving Basic Calculus: Integrals with Logarithms and Variable Limits

[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

 

[micromass]

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

 

[Robert1986]

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

 

[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.

 

[Mark44]

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

 

[genericusrnme]

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

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

 

[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