The first octant is a 3 – D Euclidean space in which all three variables namely x , y x, y x,y, and z assumes their positive values only. In a 3 – D coordinate system, the first octant is one of the total eight octants divided by the three mutually perpendicular (at a single point called the origin) coordinate planes.

Is Z 0 in the first octant?

dzdydx. z dV , where D is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant.

What is the value of Z in first octant?

Here we consider integrating the function f(x,y,z) = xz over the volume inside x² + y² = 9, in the first octant, and under the plane z = y + 2. This region is shown to the right, below.