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Evaluate e dV where E is enclosed by the paraboloid z = 5+x +y, the cylinder a2 + y = 1, and the xy plane.

Evaluate e dV where E is enclosed by the paraboloid z = 5+x +y, the cylinder a2 + y = 1, and the xy plane.

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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Evaluate e dV where E is enclosed by the paraboloid z = 5+ x² + y°, the cylinder a2 + y? 1, and the %3D ry plane.
Transcribed Image Text:Evaluate e dV where E is enclosed by the paraboloid z = 5+ x² + y°, the cylinder a2 + y? 1, and the %3D ry plane.
Expert Solution
Step 1

The objective is to evaluate ∫∫∫EezdV, where E is enclosed by the paraboloid z=5+x2+y2, the cylinder x2+y2=1, and the xy plane.

Let, x=rcosθ, y=rsinθ, z=z then dzdydx=rdrdθ

Limits of z are, z=0 to z=5+r2

Limits of r are, r=0 to r=1

Limits of θ are, θ=0 to θ=2π

Then ∫∫∫EezdV=∫θ=02π∫r=01∫z=05+r2ezrdzdrdθ

 

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