Parabolic cylindrical coordinates

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  • #1
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Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?
 

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  • #2
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Things with symmetry around an axis, like a cylinder. Try this one with cartesian coordinates, then try it with cylindrical coordinates.

[tex] \int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{2} \,\,\,(x^2+y^2)\,\,dz\,dy\,dx [/tex]
 
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  • #3
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FrogPad said:
Things with symmetry around an axis, like a cylinder. Try this one with cartesian coordinates, then try it with cylindrical coordinates.

[tex] \int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{2} \,\,\,(x^2+y^2)\,\,dz\,dy\,dx [/tex]

That works great in (circular) cylindrical coordinates, but not in parabolic cylindrical coordinates.
 
  • #4
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:blushing: hehe... sorry man.
I must have read it too quickly. Honestly, I've never worked in parabolic cylindrical coordinates.

have a good one :smile:
 

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