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Thread: simple Green's Theorem problem. please help!

  1. #1
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    simple Green's Theorem problem. please help!

    1. Find the mass of the wire.

    Density at (x,y) is x; the wire occupies the portion of the parabola
    y = (x^2)/2 from (0,0) to (1, 1/2)


    2. A wire occupies the spiral r = e^@ corresponding to @ in [0,2pi]. the density of the wire at point (r,@) is r. Find the mass of the wire.

    @ is theta btw; i don't know how to type out the symbol

    thanks
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  2. #2
    Senior Member vincisonfire's Avatar
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    $\displaystyle x= t$
    $\displaystyle y= t^2 $
    $\displaystyle rho = t $
    $\displaystyle |f'(t)| = \sqrt{1 + 4t^2}$
    $\displaystyle m = \int rho \cdot |f'(t)| dt $
    This integral must be simple enough for you
    As for number 2
    $\displaystyle x =t$
    $\displaystyle r = e^t$
    $\displaystyle rho = r = e^t $
    $\displaystyle |f'(t)| = \sqrt{1+e^{2t}}$
    $\displaystyle m = \int rho \cdot |f'(t)| dt $
    Last edited by vincisonfire; Nov 6th 2008 at 06:21 PM.
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  3. #3
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    much appreciated
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