Triple integrals in spherical coordinates

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SUMMARY

The discussion focuses on transforming triple integrals into spherical coordinates, specifically addressing the limits of the variable phi. Phi represents the angle from the positive z-axis to the negative z-axis. It is established that phi is integrated from 0 to π/2 for the upper octants and from π/2 to π for the lower octants. Understanding these limits is crucial for correctly setting up spherical coordinate integrals.

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  • Understanding of triple integrals
  • Familiarity with spherical coordinates
  • Knowledge of angular variables in polar coordinates
  • Basic calculus concepts
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  • Study the derivation of spherical coordinate transformations
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i have a question concerning transforming triple integrals into spherical coordinates. the problem is, i do not know how to find the limits of phi. Can anyone help me? Thanks...
 
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What's the problem?
 
Phi is the variable indicating the angle subtended from the positive z-axis to the negative z-axis. It is similar to theta which is usually defined from positive x, but all the way around to positive x again.

Phi is usually integrated from 0 to Pi/2 for the top four octants, and Pi/2 to Pi for the bottom four octants. Anything more than that and we'd need a problem.
 

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