# Inetgral mean for a function of 2 variables

1. Jan 12, 2007

### Methavix

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

.................pi
................./
v = (1/pi) * | v0*sin(alpha)*d(alpha) = (2/pi)*v0
................/
................0

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

thanks
Luca

Last edited: Jan 12, 2007