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Describe as a region (in any order you can) the region inside the ball $x^2+y^2+z^2=4$ and the elliptical cylinder $4x^2+z^2=1$
I know how to do the bounds of integration for a problem when given simpler planes but am not sure how to proceed on this problem.
Also, I'm not entirely sure what it means by describe but how would you describe it and/or write out the integration for a given function $f(x,y,z)$.
$$ \begin{align} -\frac{1}{2}&\le x\le \frac{1}{2},\\ -\sqrt{1-4x^2}&\le z\le \sqrt{1-4x^2},\\ -\sqrt{4-x^2-z^2}&\le y\le \sqrt{4-x^2-z^2}. \end{align} $$
