with axis being the -axis. Then it is a simple - solid, its projection on -plane being the annulus region, as shown in figure. However, it is not a simple -solid or a simple -solid. We can divide into four region by and by planes parsing through -axis and parallel to and planes.
Figure 4. Forms as a unioin of simple surfaces
51 .1.5
Example :
Let us verify Divergence theorem for the solid bounded by the paraboloid and the -plane, the vector field . The surface binding the region is , the paraboloid
-axis. Then it is a simple 
- solid, its projection on 
-plane being the annulus region, as shown in figure. However, it is not a simple 
-solid or a simple 
-solid. We can divide 
into four region by 
and 
by planes parsing through 
-axis and parallel to 
and 
planes. 
bounded by the paraboloid 
and the 
-plane, the vector field 
. The surface binding the region 
is 
, the paraboloid 
