Calc 3- Triple Integral using cylindrical coordinates

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Homework Help Overview

The problem involves evaluating a triple integral using cylindrical coordinates, specifically for the function sqrt(x^2+y^2) over a solid defined by a circular paraboloid z=9-16(x^2+y^2) and the xy-plane.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses difficulty in determining the bounds for r in cylindrical coordinates. One participant suggests drawing a cross section in the x-z plane to clarify the bounds for r as a function of z, indicating that the z bounds should also be evident from the problem.

Discussion Status

The discussion is ongoing, with participants exploring the setup of the problem and offering suggestions for visualizing the region of integration. No consensus has been reached yet.

Contextual Notes

The original poster is seeking help within the constraints of a homework assignment, which may limit the information they can provide or the methods they can use.

krtica
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Use cylindrical coordinates to evaluate the triple integral , sqrt(x^2+y^2) where the region integrated is the solid bounded by the circular paraboloid z=9-16(x^2+y^2) and the xy-plane.


I'm having trouble deciding what the bounds for r would be.
 
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try drawing a cross section, say in the x-z plane

you should be able to find r as a function of z & the z bounds should be clear from the problem
 
Thank you!
 
no worries ;)
 

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