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Simple parametrized line integral

  1. Dec 9, 2007 #1
    [SOLVED] Simple parametrized line integral

    This is from an example in my text book. They want you to evaluate the line integral:

    [tex] \int_{C} y dx + 2x dy [/tex]

    for the straight line segment in the plane from A(1, 1) to B(2, 4).

    The example says that this segment can be parametrized as x = 1 + t, and y = 1 +3t, [tex] 0 \leq t \leq 1 [/tex]. I don't know as much about parametrization as I should, so I assume I'm missing something simple here. How are they able to set up x(t) and y(t) ?

    Also, could someone explain the point of a line integral. My book shows that it can be used to find the mass of a wire given the density function of the wire. Is this all it's used for?

    Any help is appreciated.
     
  2. jcsd
  3. Dec 9, 2007 #2

    EnumaElish

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    Parametric curves "can be anything." Suppose x represents temperature and y is rainfall throughout the day. At midnight the temperature and the rainfall are both 1. As time passes, each changes with time. At the end of the day, x = 2 and y = 4.

    It can be used to measure of the total effect of any vector field along a given curve (path) in that field. See http://en.wikipedia.org/wiki/Line_integral
     
  4. Dec 9, 2007 #3
    I see, thank you for the response. It just confused me because the book didn't introduce the parametric equations until it stated the solution, which led me to believe that I was supposed to know what those curves were ahead of time.
     
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