- #1
jonroberts74
- 189
- 0
Homework Statement
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]
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, here's 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?