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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


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    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


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    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?
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