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Basic calculus question

  1. Mar 19, 2012 #1
    Hello everyone,

    I have an integral of the following form:


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



  2. jcsd
  3. Mar 19, 2012 #2


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    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


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    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


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    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,

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