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!

Path independance

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

    show that F is path independant. Then evaluate the integral F dot dr on c, where c = r(t) = (t+sin(pi)t) i + (2t + cos(pi)t) j, 0<=t<=1

    2. Relevant equations



    3. The attempt at a solution

    F = 4x^3y^2 + 2xy^3 i + 2x^4y - 3x^2y^2 + 4y^3 j

    grad f = 12x^2y^2 + 2y^3 i + 2x^4 - 6x^2y + 12y^2 j not sure i need this

    my instructor talked about numerouse way to determine path independace. which is the easiest
     
  2. jcsd
  3. May 6, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    You mean the line integral of F is path independent? All you have to do is show that the curl of F is zero. Then the result follows from Stoke's theorem.
     
  4. May 8, 2009 #3
    ok so i found the curl of F
    curl F = (8x^3y - 6xy^2 - 8x^3y + 6xy^2) = 0

    but then the problem says to eval the integral F dot dr over the region c

    when i dot them i got a extremely long expression. is this problem just a pain in the butt or did i make a boo boo
     
  5. May 8, 2009 #4

    dx

    User Avatar
    Homework Helper
    Gold Member

    You've shown that the line integral is path independent, so you can choose a more convenient path to do the integration. What does the curve C look like? What are its endpoints?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Path independance
  1. Independence of Path (Replies: 1)

  2. Independence of path (Replies: 5)

  3. Path Independence (Replies: 3)

  4. Independence of Path (Replies: 12)

Loading...