eng Science and Education Publishing American Journal of Numerical Analysis 2328-7292 2014-10-12 2 5 144 151 10.12691/ajna-2-5-2 AJNA2014252 article Kholmat M. Shadimetov 1 Abdullo R. Hayotov hayotov@mail.ru 1 Sardor I. Ismoilov 1 Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan In this paper we construct the optimal quadrature formula with polynomial weight in the Sobolev space L2(m)(0,1). Using S.L. Sobolev's method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula. http://pubs.sciepub.com/ajna/2/5/2/ajna-2-5-2.pdf optimal quadrature formulas error functional extremal function sobolev space optimal coefficients