Solve the Problem $d x$ For the Volume of the Region Enclosed by the Paraboloids

question 126

Multiple Choice

Solve the problem.
-Write an iterated triple integral in the order dz dy $d x$ for the volume of the region enclosed by the paraboloids $z = 8 - x ^ { 2 } - y ^ { 2 }$ and $z = x ^ { 2 } + y ^ { 2 }$ .

• A) \(\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 8 - x ^ { 2 } } } ^ { \sqrt { 8 - x ^ { 2 } } } \int ^ { 8 - x ^ { 2 } - y ^ { 2 } } d y ^ { 2 } d y d x\)
• B) \(\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 8 - x ^ { 2 } - y ^ { 2 } } d z d y d x\)
• C) \(\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 4 - x ^ { 2 } - y ^ { 2 } } d z d y d x\)
• D) \(\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 8 - x ^ { 2 } } } ^ { \sqrt { 8 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 4 - x ^ { 2 } - y ^ { 2 } } d z d y d x\)

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Definitions:

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A form of thinking that involves recognizing and integrating opposing viewpoints and ideas, often leading to the synthesis of a new understanding or solution.

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Difficult, perplexing, or trying situations that require a solution.

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The support for learning and problem solving that encourages independence and growth.

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The process of organizing or arranging elements in a systematic way.