Calculating ∫fdA{\displaystyle \int fdA} and ∫fdV{\displaystyle \int fdV} with angular symmetry Cyndrical: dA=2πrdz;dV=dAdr{\displaystyle dA=2\pi r\,dz;\,dV=dA\,dr}. Spherical: ∫dA=4πr2,dV=4πr2dr{\displaystyle \int dA=4\pi r^{2},\;dV=4\pi r^{2}\,dr}