#todo Then $\int \int_{S} f(x,y) \, dA =\int \int \int_{\Omega} \, dV $where $\Omega$ is the region in $\mathbb{R}^{3}$ bounded by the surface $S.$ **Informal proof**: A double integral $\int \int f(x,y) \, dA$ is the sum of the volumes of thin pillars. A triple integral $\int \int \int \, dV$ is a sum of the volume of tiny blocks. Note that $\int \int_{S} f(x,y) \, dA$ is the is the volume under the [[Algebraic Surface|algebraic surface]] $z=f(x,y)$ and over the region $S$.