Science and Education Publishing American Journal of Numerical Analysis 2328-7292 2 5 2014 10 12 Optimal Quadrature Formulas with Polynomial Weight in Sobolev Space 144 151 EN Kholmat M. Shadimetov Abdullo R. Hayotov Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan Sardor I. Ismoilov AJNA2014252 10.12691/ajna-2-5-2 2014 09 26 2014 10 08 2014 10 12 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.