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Integral problem

  1. Sep 13, 2005 #1
    Can you you solve this Integral problem

    Dear Friends
    Can youn help me to integrate the follownig formula
    L.H.S = Integrate[1-6*Lambda/x*Coth(x/2*Lambda)+12*(Lambda^2/x^2))*x^3*g(x)dx] / Integrate[x^3*g(x)dx]
    Where g(x) = a*exp[-0.5/b^2*ln(x/x0)^2] is the distribution function
    where a= 51.5801
    I like to solve for Lambda, where the L.H.S is determined experimentally
    Thank you very much for your cooperation.
    Last edited: Sep 13, 2005
  2. jcsd
  3. Sep 13, 2005 #2


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    Homework Helper

    Hey Prince. That's hard to follow. Welcome to PF. We use LaTex in here and you may wish to learn to use it if you post frequently. Check out the thread in the Physics Forum about using LaTex. This is what I think it is:

    [tex]\frac{\int_u^v \left(1-\frac{6\lambda}{x}Coth(\frac{\lambda x}{2})+12(\frac{\lambda^2}{x^2})x^3 g(x)\right)dx}{\int_u^v x^3 g(x)dx}[/tex]

    With u and v as the limits of integration

    Maybe that's close. Correct it if necessary. Really, I'd just program it into Mathematica as a function and solve it numerically:


    Plot it for starters and see where the LHS meets your value. Then can use NSolve:

    NSolve[f([itex]\lambda[/itex])==my value]

    (or whatever else it takes in Mathematica to get a numerical answer)
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