Use cylindrical coordinates to evaluate the integral $$I = \iiint_W y \, dV$$ where $W$ is the solid lying above the $xy$-plane between the cylinders $x^2+y^2 = 4$ and $x^2+y^2 = 6$ and below the plane $z = x+3$.
The calculation gives me $0$ (which I can plug in online to see is correct), but geometrically why does this make any sense?
Maybe if you think from a physical point of view it would make more sense. The integral you are trying to compute is used to get the center of mass (use density of 1, and divide by the total mass). Due to symmetry, the center of mass in the $y$ direction is at $0$