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Tricky Green's Thm Problem

  1. Jan 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Let C be a differentiable curve contained in the portion 0 ≤ x ≤ 2 of the first quadrant, starting somewhere on the positive x-axis and ending somewhere on the line x = 2. Show that the flux of the vector field F = (8xy − x^4y)i + (2x^3y^2 − 4y^2 − 3x^2 )j across C is always equal to 8.

    Let P be a point on the x-axis, Q a point on the line x=2.

    2. Relevant equations
    Div F = Mx + Ny = 0


    3. The attempt at a solution
    Using Green's Theorem, the double integral vanishes (Curl F = 0) leaving us with -[intC = - int p to 2 (3x^2)dx - int 0 to Q (0dy)] = 8 - p^3 ..... how can we eliminate the p^3 term?
     
  2. jcsd
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