the idea is let be D the unit sphere on R^3(adsbygoogle = window.adsbygoogle || []).push({});

then i wanna compute the following integral [tex] \iint _{D} f(x,y,z) [/tex]

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

[tex] \sum_ {i} \int_{0}^{1}dr f(r, \omega _{i})g(\omega _u ) [/tex]

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.

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# Approximating an integral on R^3

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