Find the volume of the region in the first octant bounded by the coordinate planes, the plane x +y = 3, and the cylinder y² + 4z² = 9. y

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
Find the volume of the region in the first octant bounded by the
coordinate planes, the plane x +y = 3, and the cylinder
y² + 4z² = 9.
y
Transcribed Image Text:Find the volume of the region in the first octant bounded by the coordinate planes, the plane x +y = 3, and the cylinder y² + 4z² = 9. y
Set up the iterated integral for evaluating
SS S₁ f(r,0,z) r dz dr de over the region D,
D
where D is the solid right cylinder whose
base is a region in the xy-plane that lies
inside the cardioid r = 4 + 4 cos 0 and
outside the circle r = 4, and whose top lies
in the plane z = 16.
16
R
D
r=4
r=4+4 cos 0
Transcribed Image Text:Set up the iterated integral for evaluating SS S₁ f(r,0,z) r dz dr de over the region D, D where D is the solid right cylinder whose base is a region in the xy-plane that lies inside the cardioid r = 4 + 4 cos 0 and outside the circle r = 4, and whose top lies in the plane z = 16. 16 R D r=4 r=4+4 cos 0
Expert Solution
Step 1: Given information

Note: As you have posted multiple questions but according to the guidelines I will answer the first question only.

Given that plane x+y=3 and cylinder y2+4z2=9

we need to determine the volume in first octant.

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