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Math Help - Line integral parameters

  1. #1
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    Line integral parameters

    I'm looking at an example in my notes where the line integral of two segments is being evaluated so (integral)C=(integral)C1+(integral)C2.

    For c1 : segment between (0,0) and (1,1)
    For c2: part of the parabola y = sqrt(x) between (1,1) and (4,2)

    for the parameterization it's written:

    c1: x(t) = t, y(t) = t, 0<=t<=1
    c2: x(t) = tē, y(t) = t, 1<=t<=2

    Can someone explain to me how to get that parameterization?
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  2. #2
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    anyone?
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  3. #3
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    http://tutorial.math.lamar.edu/Class...egralsPtI.aspx

    For segment C1, just use the line segment to vector equation:

    r(t) = (1-t)<Xo, Yo> + t<X1, Y1> where Xo,Yo are the starting points (0,0) and X1 and Y1 are the ending points (1,1).

    For segment C2, note:

    y = sqrt(x), so x = y^2. Thus, you can use y as the parameter.

    y = t, x = t^2, and y goes from 1 to 2.


    hope this helps
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