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Homework Help: 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:

    [partial](ds/dx)=sqrt(1+([partial](dy/dx))^2)
    if [partial]dx tends to 0,
    ds/dx=sqrt(1+log(dy/dx)^2)
    s=intab(sqrt(1+(dy/dx)^2))

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

    2. Relevant equations

    N/A

    3. The attempt at a solution

    N/A
     
  2. jcsd
  3. Jul 30, 2011 #2

    rock.freak667

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    Homework Helper

    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

    or

    (ΔS/Δx)2 = 1 + (Δy/Δx)2

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

    so

    [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

    rock.freak667

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    Homework Helper

    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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