Question

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

Answer 1

The integration of the function f(xyz) is 8xz over the region in the first octant above the paraboloib cylinder Z=Y^2 and below is the paraboloid z=8-2x^2-y^2 and the integration to this is ∫π20∫20∫8−r2(cos2θ+1)r2sin2θ8r3cosθsinθdzdrdθ i hope you understand my answer