Answer:
Step-by-step explanation:
The common region enclosed above the paraboloid and below the sphere is the solid.
Let's find the limit bounds for .
The region is bounded above by the sphere .
Isolate from the equation above.
On the other hand, the region is bounded below by the paraboloid
Therefore, we obtain
Now, we need to find the intersection of the sphere and the paraboloid. To do so, we need to solve the following system of equations
.
Substitute the second equation in the first equation. We obtain
Hence, the paraboloid and the sphere intersect when .
Substituting for in the equation above gives
which is a circle with a radius .
Now, we can find the bond for and .
For , we obtain
.
For , we have
.
Therefore, the needed triple integral is