Results 1 to 2 of 2

Math Help - Computing the area using parametrization

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    25

    Computing the area using parametrization

    I got stuck on this question.

    Find a parametrization of the curve x^\frac{2}{3} + y^\frac{2}{3} = 1 and use it to compute the area of the interior

    My solution:
    I set
    x=cos^3 {\theta}
    y=sin^3 {\theta}

    Then I'm stuck on how I should apply Green's Theorem.
    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 qwesl View Post
    I got stuck on this question.

    Find a parametrization of the curve x^\frac{2}{3} + y^\frac{2}{3} = 1 and use it to compute the area of the interior

    My solution:
    I set
    x=cos^3 {\theta}
    y=sin^3 {\theta}

    Then I'm stuck on how I should apply Green's Theorem.
    Green's Theorem states that

    \iint_D \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}dA = \oint_{\partial D}Pdx+Qdy

    Now there are a few combinations that work, but for example here is one. Pick P(x,y)=0,Q(x,y)=x then you get

    \iint_DdA=\oint_{\partial D}xdy=\int_{0}^{2\pi}\cos^3(\theta)(3\sin^2(\theta  )\cos(\theta))d\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 31st 2010, 11:42 AM
  2. Replies: 1
    Last Post: March 5th 2010, 04:18 AM
  3. Replies: 6
    Last Post: February 6th 2010, 06:22 AM
  4. computing area and volume with integrals
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 18th 2007, 01:45 PM
  5. computing area
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 29th 2007, 12:55 AM

Search Tags


/mathhelpforum @mathhelpforum