We consider the problem of optimization of “interval” quadrature formulas (in different statements) on the class of monotone functions defined on an interval and the problem of optimization of cubature formulas with fixed knots on classes of functions defined on a d-dimensional cube, d = 2, 3,..., and monotonically nondecreasing with respect to each variable.

We solve the problem of optimization of approximate integration of functions of two variables defined on a rectangle and monotonic in each variable by using the quadrature formulas with nodes at points of a rectangle net.