Problem $6.$ Use a triple integral to find the volume of the solid $S.$

$S$ is the solid bounded by the parabolic cylinder $x=y^2$ and the

planes $z=1-x,z=0.$

$S$ is the solid bounded by the parabolic cylinder $x=y^2$ and the

planes $x+y+z=2,z=0.$

$($a$)$ Use the order $dzdxdy.$

$($b$)$ Use the order $dxdzdy.$

$S$ is the solid bounded by the circular cylinders $x^2+y^2=4$ and

$y^2+z^2=4.$

Hint. Use the symmetry of $S.$

Recall. The volume of a solid $S$ in $3-$space is ${}_{S}1dV.$