Thanks chiro. You're quite right -- the integral over the mixture is trivially the sum of the integrals over each mixture component. It's actually those integrals I'm having trouble with.
I have a mixture of multivariate normal distributions, and I want to compute the integral with the first element of the input vector varying between specified limits, and the other elements varying from -infinity to +infinity. See attached pdf for equations. I've done it numerically but would...