Better way to integrate a gmdistribution.fit object class?

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J
J 2012-10-2
I see that objects of gmdistribution class have a cdf method that can be used indirectly to integrate Gaussian mixture models.
Is there a faster, more efficient way to integrate a gmdistribution object over an n-dimensional rectangular region of space compared to evaluating the cdf at the corners of the region and adding/subtracting those values?

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