Integrate f(x, y,z)=12xz over the region in the first octant above the parabolic cylinder z=y^2 and below the paraboloid z=8−2x^2−y^2.

The intersection of the two surfaces occurs along the cylinder , so we have the - and -coordinates of the points in the bounded region contained within and , while .

The triple integral is then given by



where denotes the bounded region in the first quadrant.

Integrating in Cartesian coordinates is easy enough to do in this order.

Element 17 is chlorine it is a group 7 element(halogen) and belongs to period 3 of the periodic table