Posted by Subhotosh Khan on September 06, 2002 at 08:25:36:
In Reply to: Calculus Box-muller Help posted by Sidd on September 06, 2002 at 02:31:23:
: I am having difficulty in solving an integral which is a part of Box-Muller Transformation.
: The integral is Int(sqrt(-2*ln(X)))dx with limits from 0 to 1
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Int(sqrt(-2*ln(X)))dx
substitute:
z^2 = -2*ln(X)
x = e^(-1/2*z^2)
dx = -z*e^(-1/2*z^2) dz
change the limits of definite integral accordingly.
Int(sqrt(-2*ln(X)))dx
=Int [z*{-z*e^(-1/2*z^2)}] dz
= [-z*{e^(-1/2*z^2)}] + int[e^(-1/2*z^2)] dz
int[e^(-1/2*z^2)] dz is a "standard" integral - with given limits integration. Look it up in any theoretical statistics (Gauss integral)or mathematical handbook.