Results 1 to 2 of 2

Math Help - Area of inside a circle but outside a cardioid

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    159

    Area of inside a circle but outside a cardioid

    I need to find the area that is inside the circle with r=1 and outside the cardioid r = 1 + SIN THETA

    I know the area of the later is 1/2 the integral of (1 + sin theta)^2 but I am having trouble with the bounds and how to deal with the circle. I would have thought it would be just pi times 1^2 times theta but.... the answer to this whole problem is 2 - pi/4 Can anyone lend a hand? THanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    The area is \int_{\pi}^{2\pi}\int_{1+\sin\theta}^1r\,drd\theta = \int_\pi^{2\pi}\left(\tfrac12-\tfrac12(1+\sin\theta)^2\right)d\theta.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: February 18th 2011, 01:48 PM
  2. Area inside cardioid and also inside circle??
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 19th 2010, 06:57 PM
  3. [SOLVED] Area inside a circle.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 7th 2010, 10:54 PM
  4. Replies: 2
    Last Post: October 9th 2008, 05:48 PM
  5. find area inside the circle
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 15th 2007, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum