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Math Help - a surface area multiple integral question..

  1. #1
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    a surface area multiple integral question..

    hello.. i do not understand this question was hoping that someone could guide me through this..

    A flat circular disc, of radius R, can be modelled as a thin disc of negligible thickness.
    It has a surface mass density function given by f(r,0) = k(1-r^2/R^2),
    where k is the surface density at the centre and r is the distance from the centre of the disc.



    Using area integral in plane polar coordinates, calculate the total mass of the disc, in kg, when R = 0.15m and k = 12 kg/m^2
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  2. #2
    Senior Member
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    Nov 2010
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    Clarksville, ARk
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    Re: a surface area multiple integral question..

    Should that be f(r, θ) = k(1-(r^2/R^2))?

    The differential for an element of area is given by dA = r dr dθ , if you're using an iterated integral.

    If you don't understand iterated integrals, then use dA = 2π r dr .

    The mass is given by: m=2\pi \int_0^R\ f(r,\theta)\,r\,dr\,.
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