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Line integral over a triangle

  1. Jun 2, 2010 #1
    1. The problem statement, all variables and given/known data

    I'm attempting Q 3 from ch 16.4 of Stewart (p 1060).

    We are required to find the line integral where C is the triangle with vertices (0,0), (1,0) and (1,2).

    The line integral is

    Int xy dx + x^2*y^3 dy

    2. Relevant equations

    3. The attempt at a solution

    I'm having trouble parametizing the vertical line between (1,0) and (1,2).

    I'd let y = 2t and x = 1, but got the wrong final answer. I suspect it's because line (1,0) to (1,2) was incorrectly expressed.

    I then wanted to integrate in terms of dy, with terminals for y of 0 and 2, and parametizing y in terms of y, but where does that leave the dx in the first part of the equation?

    I imagine it would be easier to use Green's Theorem, but the question specifically requires the use of line integrals.
  2. jcsd
  3. Jun 2, 2010 #2


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    Both parameterizations would work, but you haven't provided enough detail for us to see where you went wrong. In either case, x is a constant, so the dx term drops out.
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