Triple integral in cylindrical coordinates

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SUMMARY

The discussion focuses on solving a triple integral using cylindrical coordinates, specifically addressing the correct formulation of the volume element. The participant initially overlooked the inclusion of the radial component, represented as 'r', in the volume element formula, which is expressed as r~dz~dr~dθ. This oversight was identified and corrected, emphasizing the importance of accurately applying cylindrical coordinates in integration tasks.

PREREQUISITES
  • Understanding of triple integrals
  • Familiarity with cylindrical coordinates
  • Knowledge of volume elements in calculus
  • Basic proficiency in integration techniques
NEXT STEPS
  • Study the derivation of volume elements in different coordinate systems
  • Practice solving triple integrals using cylindrical coordinates
  • Explore applications of cylindrical coordinates in physics and engineering
  • Learn about the Jacobian transformation in multiple integrals
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable integration, as well as educators teaching integration techniques in cylindrical coordinates.

norbellys
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1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

Homework Equations

The Attempt at a Solution


image.jpg
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norbellys said:
1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

Homework Equations

The Attempt at a Solution


image.jpg
[/B]

Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.
 
LCKurtz said:
Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.
yes that was what I was missing !
 

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