Results 1 to 2 of 2

Math Help - find area of polar graph

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    71

    find area of polar graph

    the area shared by the circle r=2 and the cardiod r=2(1-cos(x))

    so it looks like the limits of integration are from -pi/2 to pi/2.

    squaring both gets 4 and 4-8cos(x)+4cos(x)^2

    i'm not sure which is supposed to subtracted from which... but i'll go 4-(4-8cos(x)+4cos(X)^2.

    which gives 8cos(x) - 4cos(x)^2

    half of that is 4cos(x) -2cos(x)^2

    then i can get 4cos(x) - 1 - cos(2x)/2

    integrating gives

    4sin(x) -x - sin(2x)/4

    and plugging in pi/2 and -pi/2 i get 8-pi. but that's not the correct answer that i've been given. where am i going wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    first off, your limits of integration are wrong. you really need to start looking at the graph of the situation.

    let r_1(\theta) = 2

    r_2(\theta) = 2(1-\cos{\theta})

    using symmetry ...

    A = 2 \int_0^{\frac{\pi}{2}} \frac{[r_2(\theta)]^2}{2} \, d\theta + 2\int_{\frac{\pi}{2}}^{\pi} \frac{[r_1(\theta)]^2}{2} \, d\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area under polar graph
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 4th 2010, 04:42 PM
  2. Polar Graph Area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 15th 2010, 09:50 AM
  3. Find the area in polar coordinates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 25th 2010, 04:59 PM
  4. find area of polar graph
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 30th 2010, 01:13 PM
  5. trying to find area in polar form
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 14th 2009, 08:12 AM

Search Tags


/mathhelpforum @mathhelpforum