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Homework Help: Describe given region

  1. Jul 23, 2014 #1
    1. The problem statement, all variables and given/known data

    I have to describe by finding the limits of integrations for x,y,z

    the region of the ball
    [tex]x^2 + y^2 +z^2 \le 4[/tex] cut by [tex]2x^2+z^2=1[/tex]

    3. The attempt at a solution
    so I can visualize these without much trouble and I used grapher so I have a working model.

    I also put in the y=0 plane because I figure "slicing" the cylinder with y_{0} is the way to go.

    so [tex] -\sqrt{4-x^2-z^2} \le y \le \sqrt{4-x^2-z^2}[/tex]

    then I can look at the y=0 plane to see the 2-D ellipse, heres a link


    now if I "slice" vertically [tex] -1 \le z \le 1[/tex] and find the change of x

    so [tex] -\sqrt{\frac{1-z^2}{2}} \le x \le \sqrt{\frac{1-z^2}{2}} [/tex]

    is that correct?
  2. jcsd
  3. Jul 23, 2014 #2
    The six inequalities you derived do indeed correctly describe the region of integration.
  4. Jul 23, 2014 #3


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    I agree with slider42 that your limits are correct, but I wouldn't consider the problem finished until you set up a triple integral (assuming you are calculating a volume) showing the order of integration with proper limits on each integral.
  5. Jul 23, 2014 #4
    yes I agree, question only asked for that but more practice is always better. I'll come back to this problem
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