1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Line integral

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data

    F=<xy, x-y> and C is the triangle joining (1,0), (0,1) and (-1,0) in the clockwise direction.

    2. Relevant equations

    How do I have the second part of this curve?

    3. The attempt at a solution
    Apparently, there should only be a sum of two integrals. So I got that curve one could be
    [tex]C_1: x=t, y=0, -1≤ t ≤ 1[/tex]

    But I have no idea how to find [tex]C_2[/tex]. There's no other way, that I see, that you can take such that you keep x constant and let y vary.
  2. jcsd
  3. Nov 8, 2011 #2
    The reason it should only be a sum of two integrals is because the line integral is just zero on the curve you have. You're only interested in the sum of the integral over [itex]C_2[/itex] and [itex]C_3[/itex]. How might you parametrize those? For example, if you wanted to find a line in x-y coordinates to go from (1,0) to (0,1), you would find its slope (-1) and its y-intercept (1). The line would be y = 1-x. So if you let x = t, then what would y be and what would t vary between?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Line integral Date
Line integral of a curve Dec 27, 2017
Line integral of a vector field Nov 29, 2017