Confused about polar integrals and setting up bounds

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Homework Help Overview

The discussion revolves around setting up polar integrals and determining the appropriate bounds for a problem involving the volume between a sphere and a cylinder. The original poster expresses confusion about how to begin and what type of integral to use.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the geometry of the problem, identifying the first surface as a sphere and the second as a cylinder. There are questions about the correctness of the equations provided and the clarity of the problem statement. Some participants suggest considering different coordinate systems for integration based on the geometry.

Discussion Status

The discussion is ongoing, with participants raising questions about the problem setup and the equations involved. Some guidance has been offered regarding the choice of coordinate systems, but there is no explicit consensus on the correct approach or interpretation of the problem.

Contextual Notes

There appears to be some confusion regarding the original problem statement, as references to specific equations have been noted as potentially missing or edited. This may affect the clarity of the discussion.

mncyapntsi
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Homework Statement
I am trying to find the volume between y = x^2+z^2 and y = 3-4x^2-2y^2.
Relevant Equations
x^2+y^2+z^2 = p^2
z^2+y^2 = r^2
So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds.
Any help would be greatly appreciated!
Thanks!!
 
Last edited:
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I assume the 3rd line, where z=8-x^2-x^2 has a mistake? Also, please write your equations in Latex.
 
WWGD said:
I assume the 3rd line, where z=8-x^2-x^2 has a mistake?
I don't see a 3rd line or this equation. Likely the OP deleted it.
 
Mark44 said:
I don't see a 3rd line or this equation. Likely the OP deleted it.
I think the problem statement was edited.
 
The first surface is a sphere. The second surface is a cylinder. So I am guessing that p2>r2 and the question is actually what volume of the sphere is outside the volume of the cylinder.

Is this correct?
Given this geometry, which type of coordinate system (cartesian, cylindrical or spherical) is appropriate for integration and why? Hint: think about cross sections. You might want to draw a figure.
 

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