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Approximating an integral on R^3

  1. Jun 8, 2009 #1
    the idea is let be D the unit sphere on R^3

    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.
     
  2. jcsd
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