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Line Integrals

  1. Dec 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Integrate h(x,y)=yi - xj over the triangle with vertices (-2,0), (2,0), (0,2) tranversed counterclockwise




    2. Relevant equations
    (1-t)a+tb




    3. The attempt at a solution
    (1-t)(-2,0)+t(2,0)=(-2+4t,0)
    (1-t)(2,0)+t(0,2)=(2-2t,2t)
    (1-t)(0,2)+t(-2,0)=(-2t,2-2t)
    integral y-x
    integral (0)-(-2+4t)*4 from 0 to 1 = 0
    integral (2t)*2-(2-2t)*-2 from 0 to 1 = 4
    integral (2-2t)*-2-(-2t)*-2 from 0 to 1 = -4
    0+4+-4=0


    I dont get the right answer, the correct answer is -8
     
    Last edited: Dec 5, 2007
  2. jcsd
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