I'll try this with some custom techniques:
First we need expression for (x,y) -values which are inside the cylinder:
$$ C = \{ (x,y) | x^2+y^2<4 \} $$
Then we need expression for "bars" from xy-plane to z=x plane:
$$ [(x,y,0) .. (x,y,x)], (x,y) \in C $$
Then we need to calculate the length of the bar:
$$ \pi_1 : (x,y) \rightarrow (x), (x,y) \in C $$
Then we just cut out bars that are $<0$:
$$ F=\{ (x) | (x,y) \in C, x\ge0 \}$$
Then area of the circle is:
$$ A = \frac{1}{2} \pi 2^2 $$
Then we should pick random point from C and calculate average:
$$ \int_{C,x\geq0}{x dC} = A \frac{\sum_{n=1}^{k}{F(x_n,y_n)}}{k}, k>10000$$, where $(x_n,y_n)$ are random point picked from $C$ so that $x\geq0$.
Picking the random point becomes possible with the following bounding box:
$$ B = ([-2..2],[-2..2]) $$ and usage of $C$ to filter out the points that do not match $x^2+y^2<4$ condition.
The bounding box needs to be adjusted for $x\geq 0$: $$B=([0..2],[-2..2])$$.