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Set up, but DO NOT EVALUATE, the integral to find the volume of the wedge cut from the cylinder $x^2 +4y^2 = 4$ above the plane $z = 0$ and below the plane $z = 3x$.

So far $$0 \le z \le 3x$$ $$0 \le x \le (4-4y^2)^{1/2}$$

I don't know how to calculate upper and lower bounds for $y$.

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At the end, $y$ travels freely, $-1$ to $1$. –  André Nicolas Nov 28 '12 at 1:57
    
How do you find y is between -1 and +1? –  Hooman Nov 28 '12 at 1:58
    
There are no constraints on $y$, except for the need to make $4-4y^2\ge 0$. –  André Nicolas Nov 28 '12 at 2:00
    
Thanks ,,, I am such an Idiot –  Hooman Nov 28 '12 at 2:01
1  
I find three-dimensional stuff not easy. In dimension two, easy, one draws a picture and everything becomes clear. In $3$-D, have to concentrate very hard. –  André Nicolas Nov 28 '12 at 2:03
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