Optimal quadrature formula in space

In this paper there is considered the problem of construction of a new optimal quadrature formula in the sense of Sard in K 2 ( P 2 ) Hilbert space, using S.L. Sobolevʼs method. There are given explicit formulas for coefficients of the optimal quadrature formula. Furthermore some numerical results are presented. The constructed optimal quadrature formula is exact for functions e − 1 2 x sin 3 2 x and e − 1 2 x cos 3 2 x .