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Help Rectangle to Cylindrical coordinate question

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



evaluate : [tex]\int\int\int_{E} e^z DV[/tex]

where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5


I just need help setting this up.

I know that theta is between 0 and 2pi

Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5).

Would the iterated integral set up in cylindrical coordinate look like this :
[tex]\int^{2\pi}_{0}[/tex][tex]\int^{\sqrt{5}}_{0}[/tex][tex]\int^{1+r}_{0}e^z dz* r*dr *d\theta[/tex]
 

Answers and Replies

  • #2
HallsofIvy
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Almost. Since the paraboloid is given by [itex]z= 1+ x^2+ y^2[/itex], the limit on z should be [itex]1+ r^2[/itex] not 1+ r.

But have you copied the problem correctly? One of the surfaces bounding the region you give as "[itex]x^2+ r^2= 5[/itex]". Was that supposed to be [itex]x^2+ y^2= 5[/itex]? If so the two surfaces do NOT completely bound a region. In your integrals you seem to be assuming that the lower boundary is z= 0. Is that given?
 
  • #3
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>>but have you copied the problem correctly? One of the surfaces bounding the region you give as x^2 + r^2 = 5.

I'm sorry its was real late, its supposed to be x^2 + y^2 = 5.

>>In your integrals you seem to be assuming that the lower boundary is z= 0. Is that given?

No, I wasn't sure so I assumed that part. It does not specify
 
  • #4
HallsofIvy
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If that is correct then there is NO region enclosed by those surfaces!
 

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