X takes the value in [a, b]), X = A, x = b.

Then the centroid coordinates (x, y) are as follows

Calculation:

x = | x(y2-y 1)dx/|(y2-y 1)dx，？

y = |( 1/2)(y2 ~ 2-y 1 ~ 2)dx/|(y2-y 1)dx

(I think the quality of the plane graph is evenly distributed, because the integral symbol cannot be input here, so it is represented by "|", and the upper and lower limits of the integral are b and a respectively. )

Extended data

The position of a point can be described by a set of numbers (ordered array). For example, on the plane, two intersecting straight lines l 1 and L2 can be drawn; Passing through any point m on the plane, make two straight lines parallel to l 1 and l2 respectively, and intersect with l2 and l 1 at P2 and P1; In this way, point M can be represented by its directed distances P2M and P 1M from l 1 to l2 and l 1. These two directed distances are called coordinates of point M, two straight lines are called coordinate axes, and the intersection of coordinate axes is called origin. When two straight lines are perpendicular to each other, it is a plane rectangular coordinate system.

In space, three intersecting planes can be made, and any point m in space can be represented by the directed distance from one of the intersecting lines passing through this point and parallel to the other plane. These three directed distances are the coordinates of a point m in space, three planes are called coordinate planes, and the intersection of any two coordinate planes is the coordinate axis. The intersection of the three axes is the origin.

Baidu encyclopedia-centroid coordinates