In postgraduate mathematics, we use definite integral to find the volume and rotate around the Y axis. Why is the formula "v=2π (integral limit) xf (x)" dx based on?
F(x) represents the curve equation in the interval where x is equal to the integral limit, and 2π represents one revolution around the Y axis (that is, 2π radians). The definite integral is the volume of the space surrounded by the above-mentioned curve rotating around the Y axis. The simplest method is to find the volume of a cylinder, that is, the volume of the space formed by a graph on the X axis surrounded by f(x)=H (constant) and Y axis, x=R and X axis around Y axis. Its integral formula is 2π (integral limit) xHdx: the upper integral limit is R, the lower integral limit is 0, and the result is π * (the square of R) * H.