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!

Finding arc length using integration

  1. Feb 20, 2014 #1
    Find the length of the positive arc of the curve [itex]y=cosh^{-1}(x)[/itex] (for which y≥0) between [itex]x=1[/itex] and [itex]x=\sqrt{5}[/itex].



    My attempt: [itex]x=cosh(y) → \frac{dx}{dy} = sinh(y) → (\frac{dx}{dy})^{2}=sinh^{2}(y)[/itex], so [itex]ds=dy\sqrt{1+sinh^{2}(y)}[/itex], therefore the arc length is [itex]S=\int_{y=0}^{y=cosh^{-1}(\sqrt{5})} cosh(y) dy= 2[/itex]. Is this right? Even if it is, is there another method of doing it (e.g. parametric equations)?
     
    Last edited by a moderator: Feb 20, 2014
  2. jcsd
  3. Feb 20, 2014 #2
    No you have to integrate between 1 and sqrt(5).
     
  4. Feb 20, 2014 #3
    But those are the x limits. If I want to integrate with respect to dy, I need y limits. I could've used dy/dx instead of dx/dy, but I don't know how to differentiate [itex]y=cosh^{-1}(x)[/itex].
     
  5. Feb 20, 2014 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Looks fine to me.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding arc length using integration
Loading...