<s>[INST] Triple Integration problem, stuck. I have a doubt over this triple integral: I have to integrate
$$\iiint x\ \text{d}x$$
between 
$$z = x^2 + y^2 ~~~~~~~ and ~~~~~~~ 4x + z = -2$$
But I feel like dumb because I cannot even start! 
It's between $z = x^2 + y^2$ and $z = -4x - 2$.
If I equal them I get
$$x^2 + y^2 + 4x + 2 = 0$$
Which I cannot solve, if it makes sense.
Cylindrical Try
$$x = R\cos\theta ~~~~~ y = R\sin\theta$$
Then it is
$$z = R^2$$
$$4R\cos\theta + R^2 = -2$$
Which means
$$R = -2\cos\theta \pm \sqrt{2}\sqrt{2\cos^2\theta + 1}$$
Right?
OR
Without cylindrical coordinates, I can solve for $y$ and $x$.
$$y^2 = z - x^2$$
and using $z = -4x -2$ I find
$$y = \pm \sqrt{2 - (x+2)^2}$$
The same for $x$ finding
$$x = -2+\sqrt{2} ~~~~~ x = -2-\sqrt{2}$$
Then I have limits, right??
 [/INST] $$I=\int_{-2-\sqrt{2}}^{-2+\sqrt{2}}\int_{-\sqrt{2-(x+2)^2}}^{\sqrt{2-(x+2)^2}}\int_{-2-4x}^{x^2+y^2}x\,dzdydx$$
let $x=-2+r\cos \theta$ and $y=r\sin\theta$
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