What kind of active speakers?

It won't affect the tweeter response much at high frequencies.

But it may help to flatten the off axis response at higher frequencies (at the expense of narrowing dispersion slightly.

The idea of sound field integration (if that's the correct term) based on distance to the listener is confusing to me. I don't have a visual image in my head as to what's going on.

Try to imagine how as a listener you are hearing the direct signal and the reflected signals. Depending on where you sit or where you place the speakers you will hear primary reflections at a different angle. If the speaker off axis curve looks just like the on axis curve ( nice and smooth and matching well if only all around lower in SPL) then the reflected energy will contribute evenly at each frequency to the overall speaker response. This means you get an even power response or you hear the same sound energy and flat frequency regardless of where you sit or where you place the speaker. Move close to one wall and you will hear more reflected energy from that particular angle - but as long as what is reflected is the same frequency response curve that is directly reaching your ears then you hear the combination which is the same sound.

If you have a speaker that beams in a narrow fashion like a flashlight at some frequencies and then widens to a broad floodlight at other frequencies (like the first example I gave) then you will be much more challenged to find a good listening position with an even response - move to one side and you may miss the side wall reflection from the narrow flashlight upper midrange but you will still get the "broad floodlight" tweeter response full in your ear - oops - all of a sudden it sounds different!

This may explain many observations where slight tweaks are adamantly claimed to produce different sounds. The mere movement of the listener a few inches (for example leaning forward) may be enough to audibly change what is heard ( a decibel or so over an octave or two is enough) and this becomes attributed to the tweak rather than being blamed on the speaker.

Of interest to the Floyd Toole fans: Published last year was "Sound Reproduction, Loudspeakers and Rooms" by Focal Press. Mr. Toole does a nice job of explaining what the title suggests. After finishing his book, my impression is that his bottom line is the best way to go for sound reproduction is multi speaker systems. Although that is not my taste, his position is well explained and hard to dispute. Regardless, it is a good read for understanding many of the topics discussed in this thread.

Musicnoise,

I have this book. It is excellent although a bit long winded for a useful reference. (Not enough math for my tastes but plenty of psychoacoustic discussions)