Solving this triple integral

  • #1

Homework Statement:

(question is attached below)

Relevant Equations:

x^2+y^2=r^2
dV=rdrdzdΘ
1593762965635.png


1593762987337.png


I am trying to solve it using cylindrical coordinates, but I am not sure whether the my description of region E is correct, whether is the value of r is 2 to 4, or have to evaluate the volume 2 times ( r from 0 to 4 minus r from 0 to 2), and whether is okay to take z from r^2/2 to 8
 

Answers and Replies

  • #2
anuttarasammyak
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[tex]\int_2^8 dz \int_0^{2z} 2\pi \rho^3 d\rho[/tex]
 
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  • #3
May I know which method did you use? I have no idea of it, thanks
 
  • #5
Delta2
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[tex]\int_2^8 dz \int_0^{2z} 2\pi \rho^3 d\rho[/tex]
Shouldn't the boundary of integration be ##\sqrt{2z}## instead of ##2z##?
 
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  • #6
anuttarasammyak
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Yes. Thanks for correction.
 
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  • #7
1593775272308.png

Can you help to see whether this is correct ? Thank you
 
  • #8
Delta2
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Yes it looks correct to me.
 
  • #13

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