Problem with a triple integral in cylindrical coordinates

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Homework Help Overview

The discussion revolves around a triple integral problem in cylindrical coordinates, specifically addressing the omission of a solution involving r=√2 in the context of a geometric region defined by a half-sphere and a paraboloid.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the necessity of visual aids, such as drawings, to better understand the problem. There are repeated inquiries about the omission of r=√2 and its implications for the solution.

Discussion Status

The conversation is ongoing, with participants actively seeking clarification on the reasoning behind the omission of r=√2. Some guidance has been offered regarding the geometric interpretation of the region involved.

Contextual Notes

Participants are navigating the constraints of the problem, particularly the conditions that define the region of integration, which includes being "below" the half-sphere and "above" the paraboloid.

Amaelle
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Homework Statement
look at the image
Relevant Equations
cylindrical coordinates
Good day
1613305455230.png

here is the solution
1613305505439.png

1613305575796.png
J just don't understand why the solution r=√2 has been omitted??
many thanks in advance
best regards!
 
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Easiest thing to do is make a drawing.
Plane z = 0 :

1613322264143.png
 
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thanks a lot and then? why sqrt(2) has been omitted?
 
The region needs to be "below" the half-sphere and "above" the paraboloid.
 
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thanks a million , you nail it!
 
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BvU said:
Easiest thing to do is make a drawing.
Plane z = 0 :

View attachment 277967
thanks a million your graph with the explantion of Charle link is just awsome!
 
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