TABLE OF CONTENTS We need the following known facts from the theory of quadrature and cubature formulas. These facts can be found, for example, in [75], [63], [21], [55].
Let ? 1 be the class of functions 
, 1, 2, ..., 1 ? p ? ?, 0 ? t ? 1, f( t) ? ? 1, and the quadrature rule
be exact on all the polynomials of order up to p - 1, and has error R n( ? 1) on the class ? 1. Let ? 2 be the class of functions 
, r = 1, 2, ..., 1 ? p ? ?, a ? x ? b, and g( x) ? 
. Then the quadrature formula
has error R n( ? 2) on the class of functions ? 2 and
([75], ) Among quadrature formulas
the best formula for the class 
(1 ? p ? ?) with ? = r - 1 and r = 1, 2, ?, or ? = r - 2 and r = 2, 4, 6, ?, is the unique formula defined by the following nodes 
and coefficients 
:
and R rq( t) is the Chebyshev polynomial 
, deviating least from zero in the norm L q(-1, 1), where p - 1 + q - 1 = 1.
