Thanks, John.... you've now probably confused even more of the readers even more....
Integrating from intake to exhaust is a nice idea but, more often than not, you don't have enough pressure data to do more than an approximation.
To me, T = m* x deltaV does it every time, with the small refinements where needed.
Otherwise, I just like looking at shock diamonds, or at the plume during a shuttle launch, when the air pressure becomes less than the pressure at the nozzle end.
CJ