Subjects/Calculus II/Applications of the integral/Mass, moments, and centroid of a laminaSection 10.9Mass, moments, and centroid of a laminaFor a region between y=f(x) and y=g(x), with constant surface density ρ:Copy LaTeXm=ρ∫ab[f(x)−g(x)]dxView detail →FormulaCopy LaTeXMy=ρ∫abx[f(x)−g(x)]dxView detail →FormulaCopy LaTeXMx=2ρ∫ab[f(x)2−g(x)2]dxView detail →FormulaCopy LaTeXxˉ=mMy,yˉ=mMx.yˉ=mMx.View detail →
For a region between y=f(x) and y=g(x), with constant surface density ρ:Copy LaTeXm=ρ∫ab[f(x)−g(x)]dxView detail →