Gives　a　methed　of　how　to　construct　the　boundary　interpolation　formnla　of　F(x,y)　in　D　which　do　not　contain　any　inner　node　and　which　also　possess　high　algebraic　exactitude　and　then　gives　a　kind　double　numerical　integration　formula　of　the　boundary　type　in　unsymmetic　region.

Remarks on a quadrature formula for a hypersingular integral;

Least square quadrature formula for singular integrals;

This paper deduces the Simpson integral formula from the formulas.

Secondly, For Cauchy singular integrals, we put forward a new style of integral formula, and Euler-Maclaurin expansion as well as extrapolation formula.

This paper makes use of the Radon seven points and five degree formulas for calculating integration to construct a class of finite element formulas for calculatin over special finite element place , at the same time provide correspondent error estimates of quadrature formulas.

A series of equivalent norms of Besov-type norm are obtained and results about the error estimate of asymptotically optimal quadrature formulas are given.

The cotes quadrature formula is widely used as it has high precision in actual calculation.