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8. Let V be the volume of the region inside the sphere r2 + y? + z? = 6 that lies above the paraboloid z = r² + y². (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and r last. DO NOT evaluate this integral. %3D

8. Let V be the volume of the region inside the sphere r2 + y? + z? = 6 that lies above the paraboloid z = r² + y². (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and r last. DO NOT evaluate this integral. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Let V be the volume of the region inside the sphere r2 +y? + z? = 6 that 2 = r? + y?. lies above the paraboloid z = (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and a last. DO NOT evaluate this integral. (b) Find the volume of the region using cylindrical coordinates.
Transcribed Image Text:8. Let V be the volume of the region inside the sphere r2 +y? + z? = 6 that 2 = r? + y?. lies above the paraboloid z = (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and a last. DO NOT evaluate this integral. (b) Find the volume of the region using cylindrical coordinates.
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