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Calculus 3 Triple Integration in Spherical Coords

  • Thread starter Wargy
  • Start date
  • #1
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Homework Statement



Use spherical coordinates to evaluate the triple integral z dV where Q is the solid that lies between x^2+y^2+z^2=1 and x^2+y^2+z^2=4.

Homework Equations


Not sure what goes here :P



The Attempt at a Solution


I've gotten everything set up, im having problems with boundaries I think. Currently I am using 0 to 2[tex]\pi[/tex] for [tex]\vartheta[/tex], 0 to [tex]\pi[/tex] for [tex]\varphi[/tex] and 1 to 2 for [tex]\rho[/tex]. When solving, I get zero as my final answer, and since I'm not clear on the conceptual meaning of a triple integral that isn't of a function that equals 1 (volume) I don't know if this answer makes sense.
 
Last edited:

Answers and Replies

  • #2
Dick
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It is zero. It's the integral of z on the volume between two spheres centered on the origin. It's as much positive as negative. The two cancel. But you should be using rho from 1 to 2.
 
  • #3
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Nevermind, read what you wrote again.
Thanks for the quick reply!
 
Last edited:
  • #4
Dick
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Makes a lot of sense.
 

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