Kinematic Formula Of Integral Geometry And Their Applications

The chord-power integrals and their applications in geometry probability are the very important theoretical achievement of integral geometry. The sequence of chord-integral reflects some significant geometrical properties. We can obtain a series of classical integral inequalities, such as the isoperimetric inequalities. The chord-integral inequalities are the development and summary of isoperimetric inequalities and the important contents of integral geometry and related disciplines. One can study the geometric invariants and geometric probability and other issues.On the basis of the definition of chord-power intergral, this paper gives the new definition of double chord-power intergral which the pair of lines intersect the convex body in integral geometry. With the method of calculus in integral geometry, it studies the relationship of double chord-power intergral and chord-power intergral. Using kinds of integral methods to discuss the calculation of double chord-power intergral, and the special inferior double chord-power intergrals are calculated by this method. Using chord-power intergral inequality. Schwarz inequality, Holder inequality and so many significant inequalities, for which it obtains a series of double chord-power intergrals separately. With the help of these double chord-power intergrals inequalities, some general case of them can be estimated. These inequalities will further develope the chord-power integral theory, and also pour into the new vigor to the integral geometry and the geometry probability.Using the radial function , the other result studied by this paper is that it calculats the value of double-power integral on disk when the power value for the even number. Still at further studies as for the power value for other situations.Finally this paper showed the application of double chord-power integral inequality from the geometry probability.