SQL Count by Active Date

SQL Count by Active Date

If I have a table of records and active/inacitve dates, is there a simple
way to count active records by month? For example:
tbl_a
id dt_active dt_inactive
a 2013-01-01 2013-08-24
b 2013-01-01 2013-07-05
c 2012-02-01 2012-01-01
If I have to generate an output of active records by month like this:
active: dt_active < first_day_of_month <= dt_inactive
month count
2013-01 2
2013-02 2
2013-03 2
2013-04 2
2013-05 2
2013-06 2
2013-07 2
2013-08 1
2013-09 0
Is there any clever way to do this besides uploading a temp table of dates
and using subqueries?