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: Find the length of the curve r = cos^2(theta/2)

  1. Jun 18, 2012 #1
    Find the length of the curve r = cos^2(theta/2)

    I'm hopelessly lost.
  2. jcsd
  3. Jun 18, 2012 #2


    Staff: Mentor

    consider a simpler case y=x^2 and what is the length from x=0 to x=10?

    dlen = (dx*dx + dy*dy) ^ (1/2) based the pythagorian theorem

    and dy= 2xdx

    so dlen = ( dx*dx + 4x^2 dx*dx ) ^ (1/2) = (1 + 4x^2) dx

    then integrate over x to get the solution

    In your equation you must consider polar coordinates so that the dlen element is:

    dlen = ( dr^2 + (r*dtheta)^2 ) ^ (1/2)

    plugin for dr and r and integrate over theta to get the length
  4. Jun 18, 2012 #3
    Thanks a lot, makes more sense! Forgive my ignorance by the way.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook