  In this study, we discuss the convergence and divergence of generalized
integrals,\int_{0}^{+\infty}\frac{sin^{b}x}{x^{a}}dx(a\epsilon R^{+},b\epsilon
N^{+}), and use the transformation method, the partial integration method, the
mathematical induction method and the complex variable residual method to
derive the calculation formulas of the two types of integrals. The calculation
formulas of the two types of integrals are unified. Finally, the convergence
criterion and the unified calculation formula of generalized integrals
of\int_{0}^{+\infty}\frac{sin^{b}x}{x^{a}}dxare obtained.
