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Line Integral

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaluate the line integral ∫(x+2y)dx+(x^2)dy, where C consists of the line segments from (0,0) to (2,1) and (2,1) to (3,0)


    2. Relevant equations



    3. The attempt at a solution

    I'm unsure of what to do. I did (1-t)r0 + t(r1) for (0,0) to (2,1) and (2,1) to (3,0). I didn't get the answer, which is 5/2 however.
     
  2. jcsd
  3. Nov 29, 2012 #2

    LCKurtz

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    Show us your work and we will help you find what went wrong.
     
  4. Nov 29, 2012 #3
    Honestly, I have no idea what to do, but here what I did.

    From (0,0) to (2,1)
    r(t) = (1-t)<0,0> + t<2,1>
    r(t) = <2t,t>

    x=2t
    y=t

    I found that the integral is from 0 to 1.

    dx/dt = 2
    dy/dt = 1

    ∫(x+2y)dx+(x^2)dy
    Then I set x as 2t and y as t into the equation:


    =∫[(2t+2t)(2)+(4t^2)(1)]dt
    =∫(8t+4t^2)dt
    = 4t^2 +4/3t^3 ] <-----evaluate from 0 to 1
    = 4 + 4/3
    = 16/3

    Then I did this same thing for the from (2,1) to (3,0) and added the two numbers.
     
  5. Nov 29, 2012 #4

    haruspex

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    I agree with 16/3, and I applied the same method for the second segment to get a total of 5/2. So your mistake must be in working you have not posted.
     
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