Evaluations of certain hypersingular integrals on interval

In this paper, we investigate a hypersingular integral on an interval. The definition of Hadamard's finite‐part integrals and some of its properties are given. Some numerical methods on approximate computation of the finite‐part integrals are constructed. The new method is very simple, easy to implement, reliable, and above all, not affected by the location of singular point. Some numerical experiments are carried out using the current formulae, and numerical results show that the current methods are feasible and effective.