I would do this as a pure analog. Check out the Wikipedia article on the Sallen-Key filter (Sallen–Key topology - Wikipedia). It's a single op-amp dual pole (12 dB/octave) filter that can be configured as low pass, band pass, or high pass. The wikipedia article is somewhat terse but has examples of all three types and appropriate math for calculating the behavior.
In order to get an analog level out of that ac signal, run it through a full-wave rectifier and a low-pass filter. Voila, DC voltage representing the total RMS energy in that band.
PS -- what I described will require either a dual supply for the op-amps or a railsplitter to give you an appropriate virtual ground for your audio input.