The Census Bureau finally released the urban/rural components of the 2010 Census data this morning. As I suspected, the weighted density of Austin's urbanized area decreased between 2000 and 2010, from 3,904 ppsm to 3,568 ppsm. The urbanized area added a bunch of people between 2000 and 2010 but proportionately few of them settled in the denser tracts in central Austin.
I'll update the calculations for the other urbanized areas when I get the time.
