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!

Homework Help: Understanding Arc Length

  1. Dec 19, 2011 #1
    1. The problem statement, all variables and given/known data

    This is probably very simple, but I'm teaching myself arc length via Paul's Online Calculus Notes and there's a simplification on the page:


    I was wondering why the first [itex]Δx^2[/itex] was simplified to 1? I understand the other [itex]Δx^2[/itex] came out of the square root.
  2. jcsd
  3. Dec 19, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What you're thinking is akin to [itex]\sqrt{a^2+b^2} = \sqrt{a^2+1}\ b[/itex], which isn't correct. You can only pull something out of a radical if it's a factor. What Paul is doing is this:
    [tex]\sqrt{\Delta x^2 + [f'(x_i^*)]^2 \Delta x^2} = \sqrt{\Delta x^2(1 + [f'(x_i^*)]^2)}[/tex]Now because Δx2 is a factor under the radical, you can say
    [tex]\sqrt{\Delta x^2(1 + [f'(x_i^*)]^2)} = \sqrt{\Delta x^2}\sqrt{1 + [f'(x_i^*)]^2}= \Delta x \sqrt{1 + [f'(x_i^*)]^2}[/tex]
  4. Dec 19, 2011 #3
    Oh you are completely right, sorry for such a silly question and thank you for explaining.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook