Oh wow, I didn't even realize that. I might fix my post, after I've tried the correct version.
KriScg's approximation was off by about the factor 2.
I think it's because you are using wrong treshold 0.004 (it was 0.04 in the presentation).
Edit: Overall, nothing really much changed, except the fact, that the approximation is still off, but not by a factor of 2. The problem is, that you want the integral to evaluate to 1 and not to "<= 1".