Consider x, when the regulator is set to zero the integrand in x reduces to y.
Is this the correct comma placement? My thinking was "Consider x" is an introductory phrase, so it is OK to place the comma after it.
Technically, that's a comma splice: two complete sentences joined by a comma. It's grammatically incorrect. You can use a colon to achieve the same effect:
"Consider x: when the regulator is set to zero the integrand in x reduces to y."