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Triple integrals, Find Volume

  • Thread starter HclGuy
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  • #1
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Homework Statement



Find the volume of the solid bounded above by [tex]\rho[/tex]=1+cos[tex]\varphi[/tex] and below by [tex]\rho[/tex]=1

Homework Equations




The Attempt at a Solution



I already solved it but was comparing my answer to my professor's solution, I was wondering why when he did the integration, his limits for [tex]\rho[/tex] were from 0 to 1, wouldn't the limits for rho be 1 to 1+cos[tex]\varphi[/tex]? Thanks
 

Answers and Replies

  • #2
HallsofIvy
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There are any number of reasons why one integral might give the same result as another- since you did not post his complete integral I don't believe we can say why his method works for this particular problem.
 
  • #3
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The thing is, I got a different answer and was not sure if the professor had made an error on the answer key since I already spotted a few other errors on it..but lets see now
[tex]\int\int_0^\pi\int_0^1\rho^2\sin\varphi d\rho d\varphi d\theta[/tex]
outer limits are from 0 to 2pi
I was just wondering why his limits for [tex]\rho[/tex] were from 0 to 1. I thought it would be from 1 to 1+cos[tex]\varphi[/tex]
 
  • #4
HallsofIvy
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You may have copied the problem wrong or he may have set it up wrong himself. Have you asked your professor?
 

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