1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Verify greens for the integral

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data

    verify greens for the integral (xy^2 i - x^2y j) dot dr over c, where c = y = x^2 from (-1,1) to (1,1). Evaluate both sides independantly to achieve the same answer

    2. Relevant equations



    3. The attempt at a solution

    so i took the partials and got

    -2xy - 2yx = -4xy, shouldnt it equal o.
     
  2. jcsd
  3. May 6, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    Re: Greens

    Why should it equal zero? What exactly is the question asking you to check?
     
  4. May 6, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Greens

    I'm confused by this. Green's theorem relates the integral around a closed path to the integral of the expression you give over the region bounded by the closed path.

    "c = y = x^2 from (-1,1) to (1,1)" is not a closed path and so does not bound a region. Did you intend to include the line from (1, 1) back to (-1, 1)?

    In any case that expression you give would be 0 only if the integral around the closed path were 0.
     
  5. May 6, 2009 #4
    Re: Greens

    ya it does say "from -1,1 to 1,1 and the line segment from 1,1 to -1,1. sorry i didnt realize that was important
     
  6. May 7, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Greens

    Then I strongly suggest you revies Green's theorem!
     
  7. May 13, 2009 #6

    benorin

    User Avatar
    Homework Helper

    Re: Verify Green

    Forgot [tex]d\vec{r}[/tex].

    Use [tex]\oint_{C}\left( xy^2\hat{i} -x^2y\hat{j}\right)\cdot d\vec{r} = \oint_{C}\left( xy^2\hat{i} -x^2y\hat{j}\right)\cdot \left( dx\hat{i} +2x\, dy\hat{j}\right) = \oint_{C}xy^2\, dx -2x^3y\, dy[/tex]
     
  8. May 13, 2009 #7
    Re: Greens

    oook check this

    [tex]\oint[/tex]xy2dx - 2x3dy

    P = xy2 Q = 2x3y

    [tex]\int[/tex][tex]\int[/tex]6x2y - 2xy dy dx

    -1 < x < 1, x2<y<1

    [tex]\int[/tex]-3x6 + x3 + 3x2 - x dx

    = 8/7
     
  9. Jun 15, 2009 #8

    benorin

    User Avatar
    Homework Helper

    Re: Greens

    [tex] \oint_{C}xy^2\, dx -2x^3y\, dy = \int_{-1}^{1}\int_{x^2}^{1}\left( \frac{\partial }{\partial x}\left( -2x^3y\right) -\frac{\partial }{\partial y}\left( xy^2\right)\right) dydx[/tex]​
    [tex]= \int_{-1}^{1}\int_{x^2}^{1}\left(-6x^2y-2xy\right) dydx = \int_{-1}^{1}\left[ y^2\left(3x^2+x\right)\right|_{y=1}^{x^2} dx[/tex]​
    [tex]= \int_{-1}^{1}\left(3x^6+x^5-3x^2-x\right) dx=-{\scriptstyle \frac{8}{7}}[/tex]​
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Verify greens for the integral
  1. Verify Green's Theorem (Replies: 1)

Loading...