Results 1 to 2 of 2

Math Help - Greens Theorem

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    San Diego
    Posts
    13

    Greens Theorem

    Greens Theorem-math-hw-9-problem-1.jpg
    How would I use Green's Theorem to prove this area integral?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2013
    From
    BC, Canada
    Posts
    100
    Thanks
    16

    Re: Greens Theorem

    Quote Originally Posted by sdsu619 View Post
    Click image for larger version. 

Name:	math hw 9 problem 1.jpg 
Views:	9 
Size:	34.0 KB 
ID:	27490
    How would I use Green's Theorem to prove this area integral?
    It is a known deduction of Green's Theorem that, for an area of a disc in a plane,

    \displaystyle A = \frac{1}{2}\oint_D xdy-ydx

    Find an expression of x and y in terms of r=f(\theta). and substitute into this equation. The only problem with this method is that this does not use Green's theorem directly, only a major consequence of it. but is probably still valid.

    For r=3\sin{2\theta},

    \displaystyle A = \frac{1}{2}\int_0^{\pi/2} r^2 d\theta = \frac{1}{2}\int_0^{\pi/2} (3\sin{2\theta})^2 d\theta = \frac{9}{2}\int_0^{\pi/2}\sin^2 2\theta d\theta = \frac{9}{2}\int_0^{\pi/2}\frac{1-cos4\theta}{2}d\theta =
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Greens Theorem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 9th 2011, 10:28 AM
  2. Greens theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 31st 2011, 01:29 AM
  3. help with greens theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 29th 2008, 12:11 AM
  4. Greens Theorem (Need Help)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 10th 2007, 05:35 PM
  5. Greens Theorem Help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 21st 2006, 06:24 PM

Search Tags


/mathhelpforum @mathhelpforum