Triple integral spherical coordinates.

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SUMMARY

The discussion focuses on solving a triple integral using spherical coordinates, specifically addressing the variables \( \rho \), \( \theta \), and \( \phi \). The user correctly identifies \( \rho \) as \( \sqrt{x^2 + y^2 + z^2} \) and seeks to determine the restrictions for the angles \( \theta \) and \( \phi \). It is established that \( \theta \) typically ranges from 0 to \( 2\pi \) and \( \phi \) ranges from 0 to \( \pi \) when dealing with spherical coordinates.

PREREQUISITES
  • Understanding of spherical coordinates in multivariable calculus
  • Familiarity with triple integrals
  • Knowledge of the relationships between Cartesian and spherical coordinates
  • Ability to visualize geometric shapes in three dimensions
NEXT STEPS
  • Study the derivation of the Jacobian for spherical coordinates in triple integrals
  • Learn how to set up and evaluate triple integrals in spherical coordinates
  • Explore applications of spherical coordinates in physics, particularly in electromagnetism
  • Investigate common mistakes when converting between coordinate systems in calculus
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Students and educators in calculus, particularly those focusing on multivariable calculus and triple integrals, as well as professionals applying these concepts in physics and engineering.

Kuma
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Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?
 
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Kuma said:

Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?

Hopefully you mean [itex]\rho=\sqrt{x^2+y^2+z^2}[/itex]. Draw a picture. What do [itex]\phi\hbox{ and }\theta[/itex] usually range through for spheres?
 

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