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Line Integrals

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data


    where C is the bent line from (0,0) to (1,1) and then to (1,0).

    2. Relevant equations

    3. The attempt at a solution

    I split the paths into two pieces. In the first one, x=t, y=t and we integrate from 0 to 1. However, for the second part, I am unable to come up with the parameterization. Please advise on how this is done.
  2. jcsd
  3. Oct 28, 2007 #2


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    Notice that in the second case, the value of x stays constant, while the value of y varies from 1 to 0. So, what parameterization suggests itself?
  4. Oct 28, 2007 #3
    Is it....

    Is it x=1 and y=t from 0 < t < 1??
  5. Oct 28, 2007 #4


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    Not quite. Remember you want y to go from 1 to 0, while t goes from 0 to 1. If you take y=t, then y goes from 0 to 1 as t goes from 0 to 1
  6. Oct 28, 2007 #5
    How about this?

    Is it x=1 and y=1-t from 0 < t < 1??
  7. Oct 28, 2007 #6


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    Yes, that works.
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