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Math Help - Finding a Constant

  1. #1
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    Finding a Constant

    Hello, One of my homework questions ask me to find the value of c where the joint density function of x,y = c*g(x^2+y^2) where g is nonnegative and the integral of g(t) from 0 to infinity converges. How would I go about answering this question if I do not know what the function g is? Any help is much appreciated.

    Thank You
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  2. #2
    MHF Contributor matheagle's Avatar
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    The double integral must equal one.
    You can switch to polar and say that

    1=c\int_0^{2\pi}\int_0^{\infty} g(r^2)rdrd\theta

    If g is only a function of r then...let

    t=r^2 and dt=2rdr

    1=c\pi\int_0^{\infty} g(t)dt

    so c={1\over \pi\int_0^{\infty} g(t)dt}
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