Then the function rotates around the Y axis, and the volume of each part is a cylinder.

The circumference of the bottom circle of the circular column is 2πx, so the bottom area is about 2π x * △ x

The height of the cylinder is f(x).

So when n tends to infinity, Vy=∫(2πx*f(x)*dx)=2π∫xf(x)dx.

Geometric development

Geometry has a long history and rich contents. It is closely related to algebra, analysis and number theory. Geometric thought is the most important thought in mathematics. The temporary development of each branch of mathematics tends to geometry, that is, to explore various mathematical theories with geometric viewpoints and thinking methods.