Best quadrature formula on Sobolev class with Chebyshev weight

Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KW r [ - 1 , 1 ] with Chebyshev weight. The given function information means that the values of a function f ∈ KW r [ - 1 , 1 ] and its derivatives up to r - 1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.