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Line integral - Advice needed

  1. Sep 16, 2011 #1
    How do you work out the parameterization for a line integral. I have this example, and the closed curve C bounds the lines y=0, x=2 and y^2 = 8x. In the solution to the problem it states that there are many parameterizations available. So I just wanted to know, how do you work out the parameterization?
     
  2. jcsd
  3. Sep 16, 2011 #2

    CompuChip

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    The easiest way is to parametrize each part separately.
    The "many parametrizations" probably refers to the fact that you can choose many different "velocities", e.g.
    x(t) = (t, 0) ([itex]0 \le t \le 1[/itex])
    x(t) = (2t, 0) ([itex]0 \le t \le 1/2[/itex])
    x(t) = (t2, 0) ([itex]0 \le t \le 1[/itex])
    x(t) = (t/2, 0) ([itex]0 \le t \le 2[/itex])
    x(t) = (1 - t, 0) ([itex]0 \le t \le 1[/itex])
    all parametrize the line segment between (0, 0) and (1, 0) (although the direction of the latter is reversed).
     
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