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Integral Limits of a function

  1. Aug 3, 2012 #1
    Hi All,

    I need your help, we we have an intergral like this

    [itex]∫^{T}_{max \in \{0, t\}}[/itex] f(x) dx

    what is the meaning of the lower limit in this integral? Thanks in advance
  2. jcsd
  3. Aug 3, 2012 #2


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    Homework Helper

    The function max(a,b) is equal to a if a > b, or b if b > a. What the lower limit of your integral means, then, is that you have a function

    [tex]g(t) = \int_{\mbox{max}(0,t)}^T dx~f(x).[/tex]

    If t is less than zero, then the lower limit is zero. If t is greater than zero, then the lower limit is t.
  4. Aug 3, 2012 #3
    Thank you @Mute, you are safer! I still have couple more questions though:

    1. How can someone arrive at this type of integral?

    2. Assuming the upper limit of the integral, T>>y, how can I implement that in my solution. In between can you please recommend a textbook/paper that I can use for this type of problem, I still have more of weird ones like this. Thanks!

  5. Aug 4, 2012 #4


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    Science Advisor

    You were the one who posted it! Where did you find it?
  6. Aug 6, 2012 #5
    I found it in a paper but the problem is that I couldn't make a sense out of how the equation of such was arrived at, so I was thinking if I could see some other example in which such equation was used, it will help to understand what I'm currently working on
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