Following Ashley’s latest comments on Chapter 5 of Introducing Monte Carlo Methods with R, I realised Example 5.5 was totally off-the-mark! Not only the representation of the likelihood should have used prod instead of mean, not only the constant should call the val argument of integrate, not only integrate uses lower and upper rather than 
Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).
