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In this paper problem of construction of optimal quadrature formulas in$W_2^{(m,m-1)}(0,1)$ space is considered. Here by using Sobolev's algorithmwhen $m=1,2$ we find the optimal coefficients of the quadrature formulas of theform $$ \int\limits_0^1\phi(x)dx\cong\sum\limits_{\beta=0}^NC_{\beta}\phi(x_{\beta}). $$

Calculation of Coefficients of the Optimal Quadrature Formulas in the $W_2^{m,m-1}(0,1)$ Space