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Math Help - Line Integral and/or Greens Theorem Problem

  1. #1
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    Line Integral and/or Greens Theorem Problem

    I have a homework question that goes like this:

     Evaluate ∫c xz ds where C is the curve with parametric equations:
    x= e-t cos(3t) y= e-t sin (3t) z=e-t 0 ≤ t ≤ 2π
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  2. #2
    Member eXist's Avatar
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    I was a little confused with the characters you used, but this is what I got from it:

    \int_C xz \,ds

    Where:
     x = (e^{-t}) cos(3t)
    y = (e^{-t}) sin(3t)
     z = (e^{-t})
     0 \le t \le 2\pi

    Then you can use greens theorem:



    Hope this helps.
    -Chad
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  3. #3
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    Quote Originally Posted by Kristen2233 View Post
    I have a homework question that goes like this:

     Evaluate ∫c xz ds where C is the curve with parametric equations:
    x= e-t cos(3t) y= e-t sin (3t) z=e-t 0 ≤ t ≤ 2π
    \int_C x z \, dr = \int_{t_1}^{t_2} x(t) z(t) \, \sqrt{ \left( \frac{dx}{dt}\right)^2 + \left( \frac{dy}{dt}\right)^2 + \left( \frac{dz}{dt}\right)^2} \, dt.
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