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Math Help - line integral

  1. #1
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    line integral

    Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -3) and the second going from (3, -3) to (6, 0).
    Computer the line integral .
    Thankyou.
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    Hello,
    Quote Originally Posted by iwonder View Post
    Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -3) and the second going from (3, -3) to (6, 0).
    Computer the line integral .
    Thankyou.
    Make a parametrization.

    Equation of line (0,0) to (3,-3) is y=-x.
    So make x=t and y=-t and substitute in the integral !
    for t going from 0 to 3 (since it's x)

    Equation of line (3,-3) to (6,0) is y=x-6.
    x=t and y=t-6
    for t going from 3 to 6.

    So this should give for the first one :
    \int_0^3 -3+3 ~ dt
    (note that since y=-t, dy=-dt)
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