A sigmoidal transformation is a one-to-one mapping of the compact interval
[0,1] onto itself whose graph is S-shaped. After giving a formal
definition, various mappings already given in the literature are reviewed in
the light of the definition. At least one new transformation is introduced
and criteria given for generating transformations having special properties.
The use of these transformations in using the trapezoidal rule to evaluate
the integral of f(x) over the limits [0,1]
is then considered and asymptotic estimates of
the truncation errors are obtained under different conditions. The paper
concludes with some numerical examples.
