Volume bounded by the surface $x=-1,\;x=1,\;y=-1,\; y=1, \; z=2,\; y^2+z^2=2$ in $R^3$
The region $z=2 $ and $y^2+z^2=2$ is confusing me. I know this is a cylinder with axis parallel to $x-axis$ and bounded above and below by $x=1$and $x=-1$ respectively. We take the projection in the $y-z$ plane.
I set up the following integral for this volume :
$$\int_{y=-1}^{1}\int_{z=\sqrt{2-y^2}}^{z=2} \int_{x=-1}^{x=1}dxdzdy$$. Is this correctly set up?