Pregunta: Example Use a double integral to find the volume: For the solid region bounded by the paraboloid 𝑧 = 4-𝑥 ^ 2-2𝑦 ^ 2 and the xy plane.

The projection of the solid is the region (say $\mathrm{R}$) in the $\mathrm{x}\mathrm{y}$-plane $\mathrm{R}=\{(\mathrm{x},\mathrm{y}):{\mathrm{x}}^2+2{\mathrm{y}}^2\le 4\}=\{(\mathrm{x},\mathrm{y}):{\left(\frac{\mathrm{x}}{2}\right)}^2+{\left(\frac{\mathrm{y}}{\sqrt{2}}\right)}^2\le 1\}$.

A sketch for this region $\mathrm{R}$ is given b...