A method for the random angly rotation of plane figures in the operation of electrical discharge wire-cutting machine was discussed.

This article employs the method of element changing in definite integral to spread the dimension formula of plane figures.

The formation of the plane figure path of the drilling and milling machine controlled by macrocomputer over mill machining;

In this paper,the area ratio of plane figure affine transformation in space is investigated,and the transformation equation of λ multiple of area is got , the area change of plane figure under affine transformation in space is studied, a important property of three axis ellipsoid is given and proved.

From commonly used equation of calculating plane figure quadrature, formulas of calculating plane figure quadrature by applying curve parametric equation can be deduced.

The cube formed after cutting one part off the same planar graph in different ways of motion and its method of calculation are introduced.

Through the comparison and analysis of four examples,this paper draws the common methods,procedures and thinking paths of using the definite integral in the calculation of the area of some planar graphs and the static pressure of the liquid.

Velocity formula and acceleration formula of point in the plane graph is proved by means of complex vector,and a simple method to obtain the velocity and acceleration is proposed.