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Inetgral mean for a function of 2 variables

  1. Jan 12, 2007 #1
    1. The problem statement, all variables and given/known data
    I have a function of two variables. I want to yield the integral mean over these 2 variables.
    In particular, the function is a vector (of constant lenght v0) coming out from a only point that can have all direction possible in a semi-space. So if i draw all vectors i draw a semi-sphere of radius v0. I call alpha one angle and beta the other one, and both of them are variable between 0 and pi.

    2. The attempt at a solution

    If a consider just a 2-dimension space i have the solution

    v = (1/pi) * | v0*sin(alpha)*d(alpha) = (2/pi)*v0

    but in the 3-D space? which is the mean vector? (that is horizontal, i mean with alpha=beta=0).

    Last edited: Jan 12, 2007
  2. jcsd
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