  We show that the low frequency absorption cross section of minimally coupled
test massless scalar fields by extremal spherically symmetric black holes in d
dimensions is equal to the horizon area, even in the presence of
string--theoretical $\alpha'$ corrections. Classically one has the relation
$\sigma = 4 G S$ between that absorption cross section and the black hole
entropy. By comparing in each case the values of the horizon area and Wald's
entropy, we discuss the validity of such relation in the presence of higher
derivative corrections for extremal black holes in many different contexts: in
the presence of electric and magnetic charges, for nonsupersymmetric and
supersymmetric black holes, in d=4 and d=5 dimensions. The examples we consider
seem to indicate that this relation is not verified in the presence of
$\alpha'$ corrections in general, although being valid in some specific cases
(electrically charged maximally supersymmetric black holes in d=5). We argue
that the relation $\sigma = 4 G S$ should in general be valid for the
absorption cross section of scalar fields which, although being independent
from the black hole solution, have their origin from string theory, and
therefore are not minimally coupled.
