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Triple Integral

  1. Jul 8, 2011 #1
    1. The problem statement, all variables and given/known data
    Been awhile since I've done them and my memory/reasoning isn't so great apparently...

    Use the triple integral to find the volume of the given solid:
    The solid enclosed by the cylinder
    [tex]x^{2} + y^{2} = 9[/tex]
    and the planes y + z = 16 and z = 1.

    2. The attempt at a solution
    Difficulty is always setting up the bounds of the integral...
    [tex]-3 \leq y \leq 3[/tex]
    [tex]1 \leq z \leq 16 - y[/tex]
    having problems with the x

    would it be:
    [tex]-\sqrt{9 - y^{2}} \leq x \leq \sqrt{9 - y^{2}}[/tex] ?
  2. jcsd
  3. Jul 8, 2011 #2


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    Sure. The planes don't intersect inside the cylinder. So you can parametrize the integral over the x,y in the circle defining the cylinder without worrying about the z value. If the planes had intersected inside the circle they would have had to give you a more elaborate description of the region.
  4. Jul 8, 2011 #3
    135*pi, cool! Thanks Dick
  5. Jul 8, 2011 #4


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    That's what I get. :)
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