Final answer:
Writing a triple integral for the volume of a region enclosed by a paraboloid requires setting up the integral in the order dz dy dx, which means integrating with respect to the variable z first, then y, and lastly x.
Step-by-step explanation:
The calculation of volumes in three-dimensional space through integrals is a fundamental concept in mathematics, particularly in multivariable calculus. When we speak about finding the volume of a region enclosed by a surface like a paraboloid, we use a triple integral. Since the question prompts us to write the triple integral in the order of integration dz dy dx, it indicates that we need to evaluate the integral by first integrating with respect to z, then y, and finally x.
While the question does not provide specific limits of integration, one would typically determine these based on the equations describing the paraboloid and other bounding surfaces. Furthermore, in practice, choosing the order of integration can greatly simplify the process, particularly if the region has a simple projection onto one of the planes. It's important to note that although the question seems to indicate a typo or irrelevant parts, understanding the order of integration is crucial regardless of the object or function you're integrating over.