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Arc Length Need Verification, If Wrong, Can You Help?

  1. May 8, 2008 #1
    1. The problem statement, all variables and given/known data

    Length of curve: y=1/2(ex-e-x) from 0 to 2


    2. Relevant equations

    s = ∫√[1+(dy/dx)^2] dx

    3. The attempt at a solution

    [sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x].
    = 3.323971
     
  2. jcsd
  3. May 8, 2008 #2

    Hootenanny

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    Gold Member

    Your notation is ambiguous. I'm guessing that your curve is,

    [tex]y(x) = \frac{e^x-e^{-x}}{2}[/tex]

    In which case it may be useful to note that,

    [tex]\frac{e^x-e^{-x}}{2} = \sinh(x)[/tex]

    Which (along with a hyperbolic identity) would greatly simplify your integrand.
     
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