approximating an integral on R^3

**zetafunction** · Jun8-09, 09:36 AM

the idea is let be D the unit sphere on R^3

then i wanna compute the following integral $LaTeX Code: \\iint _{D} f(x,y,z)$

then in order to obtain an approximate value , i make a change of variable to polar coordinates and replace the integral over angular variables by a sum so my approximate value of the integral is

$LaTeX Code: \\sum_ {i} \\int_{0}^{1}dr f(r, \\omega _{i})g(\\omega _u )$

then instead of a triple integral i have just a 1-D integral over 'r' and a sum over angular variables.

i know this can be done but is the approximation good ? , i mean if there is numerical unstabilities or you should take too many approximations over the angles.