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Help Rectangle to Cylindrical coordinate question

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data

    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]
     
  2. jcsd
  3. Nov 14, 2009 #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?
     
  4. Nov 14, 2009 #3
    >>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
     
  5. Nov 15, 2009 #4

    HallsofIvy

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    If that is correct then there is NO region enclosed by those surfaces!
     
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