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Derivation of Integral Arc Length Formula

  1. Jul 30, 2011 #1
    1. The problem statement, all variables and given/known data

    My textbook [Engineering Mathematics, Stroud, 6th Edition, page932] runs through the derivation of the integral formula for arc length. I got confused at one of the steps:

    if [partial]dx tends to 0,

    Where does the log come from and where does it go?

    2. Relevant equations


    3. The attempt at a solution

  2. jcsd
  3. Jul 30, 2011 #2


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    Could you post a scan of that page or at least that section with the derivation?

    I don't think that log is supposed to be there.

    How I learned it was in a curve if you join any two points, the 'x' distance would be Δx and the corresponding 'y' distance would be Δy. The chord length would be related as

    (ΔS)2= (Δx)2 +(Δy)2


    (ΔS/Δx)2 = 1 + (Δy/Δx)2

    as Δx→0, Δy/Δx = dy/dx and ΔS/Δx = dS/dx


    [tex]\frac{dS}{dx} = \sqrt{1+ \left( \frac{dy}{dx} \right)}[/tex]

    which you can then integrate.
  4. Jul 30, 2011 #3
    Here we go, apologies for the messy formula earlier, I didnt realize there was a Latex button.
    I was expecting exactly what you typed in the derivation, hence the confusion on my part.

    Attached Files:

  5. Jul 31, 2011 #4


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    I really don't think that 'log' should be there. Else the next step does not make sense.
  6. Aug 1, 2011 #5
    Ok, well thanks for looking it over.
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