Answered: Integration over general regions: Find…

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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Question

Integration over general regions: Find the volume of the given solid.

Enclosed by the paraboloid z = x² + y² + 1 and the planes x = 0, y = 0, z = 0,
and x + y = 4.

Expert Solution

Step 1

Consider the given paraboloid $z = x^{2} + y^{2} + 1$ and the planes $x = 0, y = 0, z = 0, and x + y = 4$ .

The plane equation can be modified as $y = 4 - x$ and it is observed from the given equations of planes that y varies from $0 to 4 - x$ and x varies from 0 to 4.

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