General Mathematics, Vol. 10,nr. 1-2, 2002
Abstract:
Our aim is to investigate a quadrature of form: \be
\label{a1} \
\ \ \ \int\limits_{0}^{1} f(x)dx= c_{1}f(x_{1})+ c_{2}f(x_{2})+
c_{3}f(x_{3})+ c_{4}f(x_{4})+ c_{5}f(x_{5})+ R(f) \ee where $f:
[0, 1]\rightarrow \RR$ is integrable, $R(f)$ is the remainder-term
and the distinct knots $x_{j}$ an supposed to be symmetric
distributed in $[0, 1]$. Under the additional hypothesis that all
$x_{j}$ an of rational type (see(4)), we are interested to find
maximum degree of exactness of such quadrature.
Full text of the article: