The "line center" should be the "center of mass", and the center of mass of a solid is the center of mass when the density is constant.

The coordinates of the solid center of mass are

x =∫∫xρ(x，y，z)dv/∫∫ρ(x，y，z)dv，

y =∫∫yρ(x，y，z)dv/∫∫ρ(x，y，z)dv，

z =∫∫zρ(x，y，z)dv/∫∫ρ(x，y，z)dv。

When the density ρ(x, y, z) is constant, the center of mass, that is, the coordinate of the center of mass, is

x =∫xdv/V，Y =∫ydv/V，Z =∫zdv/V