  We introduce a family of Cauchy integral formulas for slice and slice regular
functions on a real associative *-algebra. For each suitable choice of a real
vector subspace of the algebra, a different formula is given, in which the
domains of integration are subsets of the subspace. In particular, in the
quaternionic case, we get a volume Cauchy formula. In the Clifford algebra
case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy
formula for slice monogenic functions.
