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Stocks question(multivariable calculus)

  1. Aug 13, 2009 #1
    calculate
    [tex]
    \iint_{M}^{}rot(\vec{F})\vec{dS}
    [/tex]
    where
    [tex]
    \vec{F}=(y^2z,zx,x^2z^2)
    [/tex]
    M is a part of [math]z=x^2+y^2[/math] which is located in [math]1=x^2+y^2[/math]
    and its normal vector points outside

    i am used to solve it like this
    [tex]
    \iint_{M}^{}rot\vec{F}\vec{dS}=\iint_{D}\frac{rot\vec{F}\cdot \vec{N}}{|\vec{N}\cdot\vec{K}|}dxdy
    [/tex]
    [tex]
    \vec{N}=(2x,2y,-1)
    [/tex]
    [tex]
    \iint_{M}^{}\vec{F}\vec{dS}=\iint_{D}\frac{(-x,2xz^2-y^2,z-yz) \cdot (2x,2y,-1)}{1}dxdy
    [/tex]
    now i convert into polar coordinates

    x^2+y^2=r
    is this method ok?
     
  2. jcsd
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