Calculate [[[, (x² + y²) dædydz, (x² + y²) dxdydz, where V is limited by the surfaces x² + y² = 2z, 2 =2

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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Calculate
[ (x² + y²) dxdydz, where V is limited by the surfaces x² + y² = 2z,
=2
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Expert Solution
Step 1: Given

The given integral is triple integral subscript v open parentheses x squared plus y squared close parentheses d x space d y space d z where V is limited by the surfaces x squared plus y squared equals 2 z comma space z equals 2 .

To find the triple integral.


In cylindrical coordinates 

x equals r cos theta comma
y equals r sin theta comma
z equals z

and x squared plus y squared equals r squared .

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