Let [math]\delta=\delta\left(x,y,z\right)[/math] be the density of thin surface [math]S[/math] at the point [math](x,y,z)[/math]. Here, density is mass per unit area. [br][br]The mass of surface [math]S[/math] is[br] [math]M = \iint_{S} \delta\ d\sigma[/math].[br]The first moments about the coordinate planes:[br] [math]M_{yz} = \iint_{S} x \delta\ d\sigma[/math] [math]M_{xz} = \iint_{S} y \delta\ d\sigma[/math] [math]M_{xy} = \iint_{S} z \delta\ d\sigma[/math] [br]Coordinates of the center of mass:[br] [math]\overline{x}=M_{yz}/M[/math] [math]\overline{y}=M_{xz}/M[/math] [math]\overline{z}=M_{xy}/M[/math]

[i]This applet was developed for use with [url=https://www.pearson.com/en-us/subject-catalog/p/interactive-calculus-early-transcendentals-single-variable/P200000009666]Interactive Calculus[/url], published by Pearson.[/i]