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Complex integration

  1. Jan 23, 2015 #1
    1. The problem statement, all variables and given/known data
    The question involves finding the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t

    2. Relevant equations
    Arc length of a parametric equation ∫√(dy/dt)^2 + (dx/dt)^2 dt limits are from 0<t<3

    3. The attempt at a solution
    Taking the derivative of both x and y with respect to t and then plugging it later, I get
    ∫(2 + e^2t + e^-2t )^0.5 dt limits are from 0<t<3

    Is this the right integral? If so, how do I compute it?
     
  2. jcsd
  3. Jan 23, 2015 #2

    Dick

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    Try to factor (2 + e^2t + e^-2t ) into a perfect square.
     
  4. Jan 24, 2015 #3
    (2 + e^2t + e^-2t ) can be rewritten as e^2t(1) + 3^2t(e6^-4t) + 2(e^2t)(e^-2t) and by factoring
    e^2t(1+e^-4t+2e^-2t)
    Btw, how do I write equations in math form, because it's difficult type out exponents
     
  5. Jan 24, 2015 #4

    SteamKing

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    Look at the toolbar in the message box. It starts B I U ... and ends with ∑. Pressing the ∑ will give you access to Greek letters and other math symbols. Exponents and subscripts are accessed by pressing the x2 and x2 buttons on the toolbar.
     
  6. Jan 24, 2015 #5

    Dick

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    That's not the kind of factorization you need. You want to write it as (a+b)^2. Guess what a and b are.
     
  7. Jan 24, 2015 #6
    I just solved it! The answer is e^3 - e^-3
     
  8. Jan 24, 2015 #7
    Thank you so much
     
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