Results 1 to 8 of 8

Math Help - Stoke's Theorem

  1. #1
    Junior Member
    Joined
    Jan 2009
    From
    india
    Posts
    51

    Stoke's Theorem

    Q:let S be the surface x^2+y^2+z^2=1,z>=0.Use stokes theorem to evaluate
    line integral of (2x-y)dx-ydy-zdz
    where line integral is around circle x^2+y^2=1,z=0,oriented anti clockwise.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    See attachment
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    From
    india
    Posts
    51
    Quote Originally Posted by Calculus26 View Post
    See attachment
    every thing is clear to me except,how you calculate normal N
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,324
    Thanks
    8
    Quote Originally Posted by Calculus26 View Post
    See attachment
    This answer of \pi can't be right. If you calculate directly

    \int_c (2x-y)\,dx - y \,dy - z \,dz the vector field {\bf F} = <2x-y, -y, -z> is conservative and hence the line integral is zero!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    No the curlF is not 0 therefore the vector field is not conservative

    If it were what would the potential function be
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2009
    From
    india
    Posts
    51
    Quote Originally Posted by danny arrigo View Post
    This answer of \pi can't be right. If you calculate directly

    \int_c (2x-y)\,dx - y \,dy - z \,dz the vector field {\bf F} = <2x-y, -y, -z> is conservative and hence the line integral is zero!
    sorry F is not conservative?????
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    No F is not -- the condition is If F is conservative curl F = 0

    If you calculate the line integral directly

    z= 0 so F = (2x-y)i -yj

    note this fails the test for conservative as well since d(2x-y)/dy does not equal d(-y)/dx

    If you parameterize C by x =cos(t) y = sin(t)

    you will also get pi
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,324
    Thanks
    8
    Quote Originally Posted by Mathventure View Post
    sorry F is not conservative?????
    Quote Originally Posted by Calculus26 View Post
    No F is not -- the condition is If F is conservative curl F = 0

    If you calculate the line integral directly

    z= 0 so F = (2x-y)i -yj

    note this fails the test for conservative as well since d(2x-y)/dy does not equal d(-y)/dx

    If you parameterize C by x =cos(t) y = sin(t)

    you will also get pi
    Your both right - how silly of me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stoke's Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 9th 2011, 05:42 AM
  2. Stoke's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 11th 2010, 03:43 PM
  3. Stoke's Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 11th 2010, 06:19 AM
  4. Stoke's Theorem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 17th 2010, 10:36 AM
  5. Using Stoke's Theorem..
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 3rd 2009, 01:18 PM

Search Tags


/mathhelpforum @mathhelpforum