tape out = preout ???

Probably the tape outputs have one fixed volume so you could only control the sub's output from the volume control on the sub. The pre-outs are usually controlled by the volume control on the amp. That way you could control the volume of the main speakers and the sub from the amp's master volume control and leave the sub's volume control where it sounds best.

If you plan on using the preamp's volume control, then using the tape output to feed the sub will not work because you are tying to match a variable output with a fixed output. I doubt that you will want to get up and adjust the sub level each time you adjust the volume control. Get a Y-splitter and split the preamp output, one for the mains and one for the sub.

Plato's right on. The tape out jacks have no volume control because they have a fixed output. The preouts should work? What kind of unit is it?

What Plato said. But a little more specifically, the tape out is going to pass the signal from the source without amplification or attenuation. When you hit a loud section from the source when connected thru the tape out you could damage your speakers, etc.

What I would consider doing is to get a pair of Y splitters and connect them to the pre-out, and have one set of connectors to the amp section and the other connected to the sub. That way the VC on the Integrated would control both the amp section on the Integrated and the sub.

I'm not familiar with your Integrated, this is just generic advise so take it for what its worth.