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Line Integral (Stokes Thm)

  1. May 3, 2007 #1
    1. The problem statement, all variables and given/known data
    F = <x^2 y^3 z, sin(xyz), xyz>
    S is part of the cone y^2 = x^2 + z^2 that lies between y = 0 and y = 3.
    Oriented in the direction of the positive y-axis.

    2. Relevant equations

    3. The attempt at a solution
    I know how to do the integral, and I get the correct answer except it's the negative of the answer. My question is, what direction does "oriented in the direction of the positive y-axis" imply? I thought it was CCW, but if I do that, I get the opposite of the answer.

    I am using
    x = 3cos(t)
    y = 3
    z = 3sin(t)

    My books uses
    x = 3sin(t)
    y = 3
    z = 3cos(t)

    But I'm not sure why they would use that, unless the direction of the curve is CW...
    Last edited: May 3, 2007
  2. jcsd
  3. May 3, 2007 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    What does CCW vs. CW really mean? Imagine we have
    z axis
    ----------x axis

    and the positive y axis going into the plane. So our cross section is going to be a circle at each point of y. Oriented in the direction of the positive y-axis means the unit normal should be pointing in the positive y direction, note in this case that means it's inside the cone. So on the rim, it should travel s.t. on the inside of the cone, the surface is to your left. So your head (if you were walking around the boundary), would be pointing towards the y-axis in this case. The surface is to your left, so if you can imagine it, you would be (if standing so z=y, x=0) upside down in the picture above (if everything was drawn in). Thus, you would be looking to what we call the right, and would actually travel clockwise in this case
  4. May 3, 2007 #3
    Thank you, it was driving me nuts, now i understand
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