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!

Stokes theorem, parametrizing composite curves

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the line integral:

    F = <xz, (xy2 + 2z), (xy + z)>

    along the curve given by:

    1) x = 0, y2 + z2 = 1, z > 0, y: -1 → 1
    2) z = 0, x + y = 1, y: 1→0
    3) z = 0, x-y = 1, y: 0 → -1

    2. Relevant equations



    3. The attempt at a solution

    I don't think the problem is very difficult when just dividing the line integral into three parts, calculating each separately. But I want to be thorough to see if I got all the concepts.

    I tried to draw the curve (see attachment) which made me realize a cone cut in half would be a capping surface, so we should be able to apply Stokes theorem. But I'm having trouble parametrizing it since we've basically dealt exclusively with very standard parametrizations.

    I think that one parameter should be the height of the cone, h = [itex]\sqrt{y^{2}+z^{2}[/itex] running from 0 to 1 and the other should be the angle in the xz-plane running from 0 to [itex]\pi[/itex]. I'm just having trouble setting up the variable substitution. Can anyone give me a push?
     

    Attached Files:

  2. jcsd
  3. Sep 25, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Gauss M.D.! :smile:

    Before you spend time trying to apply stokes …

    what is the curl? :wink:
     
  4. Sep 25, 2013 #3
    <x-2,x-y,y^2>... you're saying Stokes theorem is a bad idea here?
     
  5. Sep 25, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    stokes is useful if the curl is 0, or something simple

    which do you think is easier, integrating that curl over that curved surface, or integrating the original line integral directly? :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Stokes theorem, parametrizing composite curves
  1. Stokes Theorem (Replies: 2)

  2. Stokes Theorem (Replies: 6)

Loading...