Center of Mass

To find a center of mass $(\bar{x},\bar{y},\bar{z})$

$$(\bar{x},\bar{y},\bar{z})=\left(\frac{M_{yz}}{M},\frac{M_{xz}}{M},\frac{M_{xy}}{M}\right)$$

where

$$M={\iiint }_E\delta (x,y,z)dV$$ $$M_{yz}={\iiint }_{E}x\cdot \delta (x,y,z)dV$$ $$M_{xz}={\iiint }_{E}y\cdot \delta (x,y,z)dV$$ $$M_{xy}={\iiint }_{E}z\cdot \delta (x,y,z)dV$$

and $\delta$ is a density function

See Also

Triple Integral