Results 1 to 2 of 2

Math Help - Line/Surface integral question (no computation required)

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    7

    Line/Surface integral question (no computation required)

    I just can't get my head around these line integrals and their difference.

    When do I use:

     \int_C F \cdot dr = f(B) - f(A)

    Green's theorem which is  \oint_C F\cdot T ds = \int \int (curlF) \cdot k dxdy

    Divergence theorem:  \int \int_S F \cdot n d\sigma = \int \int \int divF dV

    and Stokes theorem which is  \oint F \cdot dr = \int \int CurlF \cdot n d\sigma

    Can someone explain clearly when to use each one because to me, all the questions kind of look the same. Anyone know any tricks?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,952
    Thanks
    1629
    Quote Originally Posted by godiva View Post
    I just can't get my head around these line integrals and their difference.

    When do I use:

     \int_C F \cdot dr = f(B) - f(A)

    Green's theorem which is  \oint_C F\cdot T ds = \int \int (curlF) \cdot k dxdy

    Divergence theorem:  \int \int_S F \cdot n d\sigma = \int \int \int divF dV

    and Stokes theorem which is  \oint F \cdot dr = \int \int CurlF \cdot n d\sigma

    Can someone explain clearly when to use each one because to me, all the questions kind of look the same. Anyone know any tricks?
    The first formula is just standard formula for integration along a non-closed path- a path that has two distinct endpoints.

    Green's theorem and Stoke's theorem are almost the same- Green's theorem applies to a closed path in the xy-plane, Stoke's theorem to a closed path in three dimensions.

    The divergence theorem has nothing to do with "paths". It relates the integral on a closed surface to the integral over the region inside that surface.
    Last edited by HallsofIvy; May 25th 2010 at 03:53 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Surface integral computation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: January 11th 2012, 09:28 AM
  2. a surface area multiple integral question..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 19th 2011, 06:29 PM
  3. [SOLVED] stuck during computation of an integral
    Posted in the Calculus Forum
    Replies: 17
    Last Post: July 8th 2011, 02:35 PM
  4. Surface integral question...
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 21st 2010, 02:17 AM
  5. Help Question Surface Integral Space
    Posted in the Calculus Forum
    Replies: 0
    Last Post: May 9th 2009, 09:29 PM

Search Tags


/mathhelpforum @mathhelpforum