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Calculate between [-epsilon,epsilon]

  1. Nov 26, 2009 #1
    i need to integrate

    [tex]-(p(y)f(y)')'=m^2w(y)f(y)[/tex]
    where
    [tex]p(y)=e^{4ky}(1-4ak^2)[/tex] and [tex]w=-4ae^{2y}k\delta(y)[/tex]

    but y between [0,infinity[

    ¿i calculate between [tex]\int^{epsilon}_0????[/tex] or ¿i calculate between [-epsilon,epsilon]?????

    but, what is??

    [tex]\int^{\epsilon}_0(p(y)f(y)')'dy[/tex]

    whit f is not continuous in zero


    the result is
    [tex]f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}[/tex]
     
    Last edited: Nov 26, 2009
  2. jcsd
  3. Nov 26, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: question

    I have no idea what you are talking about. What are yu integrating? If you are talking about the integral above, if it is given as a definite integral, you use whatever limits of integration are given. If it is given as an indefinite integral (anti-derivative) you do not use any limits of integration.

    By the Fundamental Theorem of Calculus, the integral of the derivative of any function is that function:
    [tex]\int^{\epsilon}_0(p(y)f(y)')'dy= p(y)f(y)' [/tex]


    If f is not continuous at zero, then it is not differentiable at zero and the integrand above does not exist at 0.


    Since you haven't actually stated what the problem is, I have no idea whether that is correct or not.
     
  4. Nov 26, 2009 #3
    Re: question

    [tex]f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}[/tex]
    this problem is in eq. (3)-(6)......(10)
    of:
    http://arxiv.org/PS_cache/hep-th/pdf/0311/0311267v3.pdf
     
    Last edited by a moderator: Apr 24, 2017
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