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The average of a function

  1. Mar 19, 2005 #1
    I have this function:
    y=x/(x-1/x)
    and I want to find out the average value of y, between two values of x.

    Is there some mathematical way to do this?
     
  2. jcsd
  3. Mar 19, 2005 #2

    cronxeh

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    [tex]\frac{1}{x_{2}-x_{1}} \int_{x_{1}}^{x_{2}} {\frac{x}{x-\frac{1}{x}} dx }[/tex]

    [tex] a = x_{1}, b = x_{2} [/tex]

    [tex]\frac{1}{b-a} * ( b + \frac{1}{2}*log(b - 1) - \frac{1}{2}*log(b+1) - a - \frac{1}{2} * log(a-1) + \frac{1}{2} * log(a+1) ) [/tex]
     
    Last edited: Mar 19, 2005
  4. Mar 19, 2005 #3

    Zurtex

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    Correct me if I am wrong but I think that nicely cancels down to:

    [tex]\frac{1}{b - a}\left(b - a + \text{tanh}^{-1}(a) - \text{tanh}^{-1}(b) \right)[/tex]
     
    Last edited: Mar 19, 2005
  5. Mar 19, 2005 #4

    cronxeh

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    And you assume that if OP doesnt know the avg of a function, then he'll know what hyperbolic tangent is :rofl:
     
  6. Mar 19, 2005 #5
    I know what tanh is but not the average of a function.
     
  7. Mar 19, 2005 #6
    Ah, but do you know what [tex]\tanh^{-1}[/tex] is?!?!
     
  8. Mar 21, 2005 #7

    HallsofIvy

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    The average of a function, f(x), between x= x1 and x= x2 is:
    [tex]\frac{1}{x_2-x_1}\int_{x_1}^{x_2}f(x)dx[/tex]
     
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