Solving Volume Problems in Physics: Cartesian vs. Spherical Coordinates

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SUMMARY

The discussion focuses on solving volume problems in physics using Cartesian and spherical coordinates. The user initially attempted to compute the volume of a set A using Cartesian coordinates, resulting in complex integrals. A subsequent attempt using spherical coordinates also yielded unsatisfactory results. The consensus is that the user did not select the optimal approach for the problem at hand, indicating a need for better understanding of coordinate systems in volume calculations.

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  • Understanding of Cartesian coordinates in calculus
  • Familiarity with spherical coordinates and their applications
  • Basic knowledge of integral calculus
  • Experience with volume computation techniques
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  • Study the conversion between Cartesian and spherical coordinates
  • Learn about the Jacobian determinant in coordinate transformations
  • Explore specific volume problems using spherical coordinates
  • Review integral calculus techniques for simplifying complex integrals
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Students and educators in physics and mathematics, particularly those tackling volume problems and seeking to improve their understanding of coordinate systems in calculus.

twoflower
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Hi,

been solving another volume problem here and though it seemed very straightforward, I'm getting very ugly integrals so it rather seems that I haven't chosen appropriate approach. I scanned how I did it, first in cartesian coordinates:

http://twoflower.matfyz.cz/inc/int.cartesian.jpg"

and then in spherical coordinates:

http://twoflower.matfyz.cz/inc/int.polar.jpg"

Neither of them seems useful...or maybe I'm substituting it wrongly.

A is the set the volume of which I'm trying to compute.

Thank you for any advices.
 
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I got it, I really didn't choose the best approach.
 

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