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: Integrating to find the length of a Cardiot Curve

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data
    find the length of the cardiot r = 1+cos(Θ)

    I'm going to use { as the integral sign
    all integrals are definite between 0 and Pi

    2. Relevant equations
    L = 2 {sqrt[(r^2(Θ))+(dr/dΘ)^2]dΘ

    3. The attempt at a solution
    L=2* {sqrt[2+2cos(Θ)] dΘ

    I'm having a really hard time trying to integrate sqrt[2+2cos(Θ)] dΘ and was hoping someone could explain to me how you integrate that.

  2. jcsd
  3. Nov 28, 2009 #2
    Personally, I would start by doing

    \int_0^\pi \sqrt{2 + 2\cos\theta} \, d\theta
    = \sqrt{2}\int_0^\pi \sqrt{1 + \cos\theta}\, d\theta.

    It's totally not necessary, but it sort of simplifies things. Then you want to use the identity
    \frac{1 + \cos\theta}{2} = \cos^2\frac{\theta}{2}

    Multiply both sides of that identity by 2, then you'll have something a little nicer to work with..
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook