Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic calculus question

  1. Mar 19, 2012 #1
    Hello everyone,

    I have an integral of the following form:

    log([itex]\int_{r}^{\inf}\frac{P(r,f)}{P(f)}dr)[/itex]

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

    [itex]\frac{1}{P(f)}[/itex]log([itex]\int_{r}^{\inf}P(r,f)dr)[/itex]

    Thanks,

    Luca
     
  2. jcsd
  3. Mar 19, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    You can bring it outside the integral.
    But you also brought it outside the log, which is wrong.
     
  4. Mar 19, 2012 #3
    Outside of the integral? Yes. Outside of the log? no.
     
  5. Mar 19, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

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

    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.
     
  6. Mar 19, 2012 #5

    Mark44

    Staff: Mentor

    Also, since P(r, f) and P(f) appear to be different functions with different domains, they should have different names.
     
  7. Mar 19, 2012 #6
    It could be that [itex]P(f) \equiv P(r_0 , f)[/itex] for some fixed [itex]r_0[/itex], I've seen that used quite a lot.
     
  8. Mar 19, 2012 #7
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Basic calculus question
Loading...