Results 1 to 2 of 2

Math Help - Green's Theorem

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    64

    Green's Theorem

    I'm just trying to learn Green's Theorem. Can somebody look this over and see if I've got it right?

    Question:

    Let R be a region bounded by the curve and line

    y=-x^2+3x-2 and y=-2

    Verify Green's theorem in the plane for

    \oint_{\partial{R}} (x-y)dx (x-y)dy

    For the region I found  0 \le x\le 3 and -2 \le y \le 1/4

    So:

    \int_0^3 \int_{-2}^{\frac{1}{4}} \frac{\partial}{\partial x}(x-y)-\frac{\partial}{\partial y}(x-y)dydx

    =\int_0^3 \int_{-2}^{\frac{1}{4}}2dydx

    =\int_0^3 \frac{9}{2} dx = \frac{27}{2}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    The integrand is correct but the limits are not--the region is not a rectangle

    See attachment

    You can also verify by computing the line integral directly though in this case it would be some work
    Attached Thumbnails Attached Thumbnails Green's Theorem-green-sthm.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Green's Theorem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 26th 2010, 09:11 AM
  2. Greenís theorem
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: November 9th 2009, 02:58 AM
  3. Green's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 6th 2009, 11:24 AM
  4. Theorem of Green
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 26th 2009, 04:38 PM
  5. Green's theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 23rd 2009, 02:23 PM

Search Tags


/mathhelpforum @mathhelpforum