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Line Integrals

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data
    The problem is given in the following image.
    http://img46.imageshack.us/img46/2972/lskfjsf.png [Broken]


    2. Relevant equations
    ∫h(r)*dr = ∫h[r(u)]*r'(u)du


    3. The attempt at a solution
    I was able to figure out plugging in (t^2+3) at every x and sin(1/2πt) at every y. I then set up the dot product of the substituted equation and r'(u)du (2t + 1/2πcos(1/2πt)). The problem is, the integral ends up being much to complex to work by hand since I'm not allowed to use a calculator for this problem. So I was wondering if there was an easier way to work this problem out?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 9, 2011 #2

    LCKurtz

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    Think about why the first part asked you to find f(x,y) whose gradient is the given vector field. Perhaps you can use that f(x,y) somehow, hint, hint.
     
    Last edited by a moderator: May 5, 2017
  4. Dec 9, 2011 #3
    Okay, so I found f(x,y) to be:
    3x + e^x*y^2 + 3e^x*y + 2e^x + y^2
    But I'm still confused on where to continue with that.
     
  5. Dec 9, 2011 #4

    LCKurtz

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    Your text should have a theorem about evaluating line integrals when you have a potential function f(x,y), and that is the whole point of this problem.
     
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