1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why the modulus signs when integrating f'(x)/f(x)?

  1. Jan 3, 2005 #1
    I am able to proove to myself, through generalised substitution, that the integral of f'(x)/f(x) is lnf(x)+c, but where do the modulus signs come from? ie - The accepted integral is ln|f(x)|+c, not lnf(x)+c

    Thanks in advance. :smile:
  2. jcsd
  3. Jan 3, 2005 #2
    I cannot be specific in my answer, but I know that a negative argument will not work with the natural logarithm function, therefore I guess the magnitude of the answer is the argument that is valid.
  4. Jan 3, 2005 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    logarithms are only defined for positive arguments: loga(x) is the inverse to ax and (for a positive) ax is always positive.

    But d(ln(x))/dx= 1/x for x positive, and using the chain rule, d(ln(-x))/dx= (1/(-x))(-1)= 1/x with x negative. Thus: the anti-derivative for ln(x) is properly ln|x|+ C rather than ln(x)+ C.

    I will confess that I always forget the "| |" myself. Most of the time it doesn't matter: [itex]\int_a^b (1/x)dx= ln b- ln a[/itex] if a and b are both positive,
    ln(|b|)- ln(|a|)= ln(-b)- ln(-a) if a and b are both negative so you can just 'ignore' the negative signs. Of course, 1/x is not defined for x= 0 and the integral is not defined if a is negative and b positive.
    Last edited: Jan 3, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Why the modulus signs when integrating f'(x)/f(x)?
  1. F(g(x))dg(x) integral (Replies: 1)