The main aim is to obtain integral formulas for DAHA coinvariants and the
corresponding inner products for any values of the DAHA parameters. In the
compact case, our approach is similar to the procedure of ``picking up
residues" due to Arthur, Heckman, Opdam and others; the resulting formula is a
sum of integrals over double affine residual subtori. A single real integral
provides the required formula in the noncompact case. As q tends to 0, our
integral formulas result in the trace formulas for the corresponding AHA, which
calculate the Plancherel measures for the spherical parts of the regular AHA
modules. The paper contains a systematic theory of DAHA coinvariants, including
various results on the affine symmetrizers and induced DAHA modules.Comment: 53 pages, 2 figure