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Line Integral

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    A curve lamda starts in (0,0) and fallows a straight line from x = 0, y = 0 to x = 1, y = 0 and then another straight line to x = 2 and y = 1. Calculate the line integral I = S vdr
    where S is an integral s
    v = (x+3y)i + (3+y)j
    2. Relevant equations



    3. The attempt at a solution

    the first line
    y = 0
    dy = 0
    S x dx from 0 to 1
    = 1/2

    The second line
    x = t
    y = t
    dx = dt
    dy = dt

    S (t+3t)dt + (3+t)dt
    and here it stops. Both x and y are variables and x are supposed to go from 1 to 2 and y from 0 to 1.
     
  2. jcsd
  3. Apr 26, 2009 #2

    Dick

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    x=t and y=t doesn't parametrize the line connecting (1,0) and (2,1), does it?
     
  4. Apr 26, 2009 #3
    then there is something I have got wronge. I have not done much of parametrization, but I was thinking a straight line from (1,0) to (2,1) had to be 45 degrees and the you used x = t and y = t which gives 45 degree angle.
     
  5. Apr 26, 2009 #4

    Dick

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    It's 45 degree's alright but if you put t=0, you get (0,0). How about putting x=t+1?
     
  6. Apr 26, 2009 #5
    So it is?

    x = t+1
    y = t
    dx = dt
    dy = dt
    S t+1 + 3t + 3 + t dt
    S 5t + 4 dt from 0 to 1
    = 13/2

    Thanks for all the help
     
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