Results 1 to 2 of 2

Math Help - Polar Curves - Enclosed Area

  1. #1
    Del
    Del is offline
    Member
    Joined
    Nov 2007
    Posts
    83

    Polar Curves - Enclosed Area

    Find the area of the region inside
    r = 11 sinθ but outside r = 1.

    Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Del View Post
    Find the area of the region inside
    r = 11 sinθ but outside r = 1.

    Please help!
    Setting them equal to get the points of intersection we get

    11\sin(\theta)=1 \iff \sin(\theta)=\frac{1}{11} \iff \theta =\sin^{-1}\left( \frac{1}{11}\right)

    This is the reference angle in the second quadrant so the upper limit of integration is \pi-\sin(1/11)

    A=\frac{1}{2}\int_{\sin^{-1}(1/11)}^{\pi-\sin^{-1}(1/11)}((11\sin(\theta))^2-1^2)d\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. finding area enclosed by the curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 14th 2011, 06:44 PM
  2. Area enclosed by two curves
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 6th 2011, 09:20 PM
  3. How to find the area enclosed by two curves?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 12th 2009, 12:49 PM
  4. Find the area enclosed by the given curves
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 11th 2009, 03:56 PM
  5. Area enclosed by two curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 7th 2009, 07:24 PM

Search Tags


/mathhelpforum @mathhelpforum