Results 1 to 4 of 4

Math Help - find area inside the circle

  1. #1
    Senior Member
    Joined
    Jan 2007
    Posts
    477

    find area inside the circle

    Find the area of the region that is inside the circle r = 6cos(theta) but outside the cardoid r = 2 + 2cos(theta)

    pic looks like this: http://us.st11.yimg.com/us.st.yimg.c...s_1932_3273205

    needing help with this one please.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, rcmango!

    Find the area of the region that is inside the circle: .r = 6Ěcosθ
    but outside the cardoid: .r = 2 + 2Ěcosθ
    Code:
                            |
                           **
                       *    |    *
                     *      |       * * *
                    *       |   *     *:::::*
                    *       | *         *:::::*
                     *      |*           *:::::*
                       *    |              :::::
                         *  *             *:::::*
              - - - - - - - * - - - - - - *:::::*
                         *  *             *:::::* 
                       *    |              :::::-
                     *      |*           *:::::*
                    *       | *         *:::::*
                    *       |   *     *:::::*
                     *      |       * * *
                       *    |    *
                           **
                            |

    Find the intersections of the two curves.

    . . 6Ěcosθ .= .2 + 2Ěcosθ . . 4Ěcosθ .= .2

    . . cosθ .= .1/2 . . θ .= .▒π/3

    Due to the symmetry, we can integrate from 0 to π/3 and multiply by 2.


    A . = . 2 x (1/2)
    [(6Ěcosθ)▓ - (2 + 2Ěcosθ)▓] dθ


    Can you finish it now?

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2007
    Posts
    477
    i'm not good at integrals, but i'm working on it. thankyou!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2007
    Posts
    477
    ..still working on it.
    Last edited by rcmango; February 15th 2007 at 12:43 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 23rd 2011, 06:18 PM
  2. Area inside cardioid and also inside circle??
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 19th 2010, 05:57 PM
  3. [SOLVED] Area inside a circle.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 7th 2010, 09:54 PM
  4. Area of inside a circle but outside a cardioid
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 4th 2008, 12:29 AM
  5. Replies: 2
    Last Post: October 9th 2008, 04:48 PM

Search Tags


/mathhelpforum @mathhelpforum