1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivation of Integral Arc Length Formula
Loading...