Home/Calculus II/Mass, moments, and centroid of a lamina/Formula10.9. Mass, moments, and centroid of a laminaFormulaIn 10.9. Mass, moments, and centroid of a laminaFormulaCopy LaTeXxˉ=Mym,yˉ=Mxm.\bar{x}=\frac{M_y}{m}, \qquad \bar{y}=\frac{M_x}{m}.xˉ=mMy,yˉ=mMx.TagsantiderivativeApplicationapplications integral mass moments and centroid of a laminaareavolumenVariablesxxxVariable independiente (variable de integración)mmmExponente o índice enteroConditionsyˉ=Mxm.\bar{y}=\frac{M_x}{m}.yˉ=mMx.Found an error? Contact us.Related formulasRelatedFormulaMx=ρ2∫ab[f(x)2−g(x)2] dxM_x=\frac{\rho}{2}\int_a^b[f(x)^2-g(x)^2] \,dxMx=2ρ∫ab[f(x)2−g(x)2]dxOpen formulaOpen in sectionRelatedFormulaMy=ρ∫abx[f(x)−g(x)] dxM_y=\rho\int_a^b x[f(x)-g(x)]\,dxMy=ρ∫abx[f(x)−g(x)]dxOpen formulaOpen in sectionRelatedFor a region between y=f(x)y=f(x)y=f(x) and y=g(x)y=g(x)y=g(x), with constant surface density ρ\rhoρ:m=ρ∫ab[f(x)−g(x)] dxm=\rho\int_a^b[f(x)-g(x)]\,dxm=ρ∫ab[f(x)−g(x)]dxOpen formulaOpen in section