# Finding a Constant

• November 8th 2009, 06:25 PM
stats1234
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
• November 8th 2009, 10:58 PM
matheagle
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 $c={1\over \pi\int_0^{\infty} g(t)dt}$