High number | summary of calculation methods of volume of rotating body, double integral calculation of volume of rotating body

The so-called rotating body , It refers to a three-dimensional figure formed by a plane figure rotating around a straight line in the plane , The volume of the rotating body is the volume of the solid figure .

  One 、 Calculation method of volume of rotating body

  Advanced Mathematics | Application of definite integral Cylindrical shell method Cylindrical method _ Xipiyou's blog -CSDN Blog _ Definite integral applies cylindrical shell method

  Two 、 Volume calculation methods of other types of rotating bodies

1. Two curves form a region around x Volume of the rotating body of the shaft （ Disjoint )

 

2. Two curves form a region around y Volume of the rotating body of the shaft （ The intersection )

3. The plane figure is wrapped around y Calculation of the volume of the rotating body of the shaft  

 4. The rotation axis is not the type of coordinate axis

Within the scope of postgraduate entrance examination , Even if the axis of rotation is not the horizontal and vertical axis , It is also a straight line parallel to the coordinate axis .

There are two ways to deal with ： Infinitesimal method and translational method .

 

 

  3、 ... and 、 Calculate the volume of a rotating body by double integral

Advanced Mathematics | 【 Multiple integral 】 Classic questions And Li Lin 880 Detailed explanation _ Xipiyou's blog -CSDN Blog