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Math Help - how long is this cable? arc length question

  1. #1
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    how long is this cable? arc length question

    question:A telephone cable susbended between two poles 20 meters appart hangs in a curve with equation: y=10(e^{\frac{x}{20}}+e^{\frac{-x}{20}}) where -10<=x<=10

    how long is the cable?

    work:using the formula L=2\int_0^{10} \sqrt{1+(\frac{dy}{dx})^2}dx

    this gives me an impossible (beyond my level) integral to solve
    Last edited by superdude; November 12th 2009 at 04:45 PM. Reason: latex
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  2. #2
    MHF Contributor chisigma's Avatar
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    The problem can be easily solved remembering some properties of the hyperbolic functions. In fact is...

     y= 20 \cdot \cosh \frac{x}{20} (1)

    ... so that is...

    \frac{dy}{dx}= \sinh \frac{x}{20} (2)

    (\frac{dy}{dx})^{2} = \sinh^{2} \frac{x}{20} = \cosh^{2} \frac{x}{20} -1 (3)

    Kind regards

    \chi \sigma
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  3. #3
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    could someone elaborate on a differnt approach? I haven't learned about hyperbolic functions
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