Solving this triple integral

  • #1
daphnelee-mh
66
4
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]
 
  • #3
daphnelee-mh
66
4
May I know which method did you use? I have no idea of it, thanks
 
  • #4
anuttarasammyak
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Find attached my handwriting.
 

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  • #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.
 
  • #7
daphnelee-mh
66
4
1593775272308.png

Can you help to see whether this is correct ? Thank you
 
  • #9
daphnelee-mh
66
4
Thank you so much
 
  • #11
daphnelee-mh
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  • #13
daphnelee-mh
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