Results 1 to 3 of 3

Math Help - Area Between Polar Curves

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    36

    Area Between Polar Curves

    I am having troubles finding the area between two curves from 0 to 2 \pi:

    The inside of r=1+cosθ and the outside of r=2cosθ

    Is it possible to simply subtract 2cosθ from 1+cosθ and take the integral of that so it looks like:

    \frac{1}{2} \int_0^{2\pi} (1-cos\theta)^2d\theta

    Thanks ahead of time for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    Look at the sketch below
    The area is twice the one for \theta between 0 and \pi and the latter can be split into 2 parts : \theta between 0 and \frac{\pi}{2} and \theta between \frac{\pi}{2} and \pi

    For \theta between 0 and \frac{\pi}{2} the radius varies between 2 \cos \theta and 1 + \cos \theta

    For \theta between \frac{\pi}{2} and \pi the radius varies between 0 and 1 + \cos \theta

    Therefore

    A = 2 \left(\int_{0}^{\frac{\pi}{2}} \int_{2 \cos \theta}^{1 + \cos \theta} r dr d\theta + \int_{\frac{\pi}{2}}^{\pi} \int_{0}^{1 + \cos \theta} r dr d\theta\right)

    I can find A = \frac{\pi}{2} which seems possible when looking at the figure

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    36
    Thank you very much, that helped out tremendously
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area between two polar curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 2nd 2010, 06:11 PM
  2. area of polar curves
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 11th 2010, 05:54 PM
  3. Area of polar curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 11th 2009, 12:19 AM
  4. Area Between Polar Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 25th 2009, 05:42 AM
  5. Area between Polar Curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 24th 2008, 11:30 PM

Search Tags


/mathhelpforum @mathhelpforum