Find the volume of the region common to the interiors of the cylinders First cylinder $x^2+y^2=4$
Second cyclinder $x^2+z^2=4$
My progress so far
$$V=8\int_0^2\int_0^\sqrt{4-y^2}\int_0^\sqrt{4-x^2}dzdxdy$$
I know I can substitute $x$ with $2\sin(\theta)$ in $\int\sqrt{2-x^2}$ but if I do that then I came across $sin(4\sin\theta)$ after substituting $y$ with $2\sin\theta$ in $\int_0^\sqrt{4-y^2}\cos^2\theta$

You may use a triple integral to find the volume.
$$ V= 8\int _0^2 \int _0^{\sqrt {4-x^2}}\int _0^{\sqrt {4-x^2}}dzdydx$$
