1, the projection method first determines the maximum projection plane d, and then divides the projection plane into infinitesimals to get some columns with curved tops, and the whole integration area is tiled by columns. This process can also be called "first-in-first-out-second method"-first definite integral along the height direction of the curved top cylinder, and then double integral on the maximum projection plane.

2. Section method

Firstly, the integration range along a certain axis (for example, z 1≤z≤z2, where z 1, z2 is a constant) is determined, and then the integration area with the cross section perpendicular to the axis is intercepted to obtain a thin slice, and the whole integration area is formed by stacking the cross section D_z of the layer. This process can also be called "the first two and the last one"-first, double integration in the thin area, and then definite integration along the axis determined at the beginning.

Think of them as cutting bread, the projection method is cut into pieces, and the section method is cut into layers. The map you gave is an accurate projection method, so you can experience it. Your other question, I calculated it by section method (of course, you can also use projection method, you can try it).