QuadGK returning zero when bounds Inf

General Usage
1

Any help understanding the behavior of QuadGK here would be greatly appreciated. I have two well behaved functions, pdf(Normal(1.,0.1),x) and cdf(Normal(-3.,0.1),x) and I’d like to integrate their product.

quadgk(x -> pdf(Normal(1.,0.1),x)*cdf(Normal(-3.,0.1),x), -50., 50.)

returns (1.0000000000047264, 5.928947342456714e-9), more or less as expected, but

quadgk(x -> pdf(Normal(1.,0.1),x)*cdf(Normal(-3.,0.1),x), -50., Inf)

returns (0.0, 0.0). I would have expected to get 1 again since there isn’t much going on in the region [50,Inf].

2

Indeed, the integrand is basically zero for the majority of the interval. I think QuadGK samples quadrature nodes adaptively and misses the region where the integrand is non-zero. I also run into this from time to time when numerically computing CDFs by integrating PDFs. I think I solved this by adding a few additional quadrature nodes around the mode:

quadgk(x->.., -50, MODE, Inf)

This usually works fine.