1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    http://www.wolframalpha.com/input/?i=plot+x^2+++z^2/2+=1/2

    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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted