원통 좌표계 사용: 0 \le r \le 2,\; 0 \le \theta \le \pi/2,\; 0 \le z \le r\sin\theta.

\displaystyle\iiint_E y\, dV= \int_0^{\pi/2} \int_0^2 \int_0^{r\sin\theta} (r\sin\theta)\, r\, dz\, dr\, d\theta

= \displaystyle\int_0^{\pi/2} 4\sin^2\theta\, d\theta= 2\left[ \theta - \tfrac{1}{2}\sin 2\theta \right]_0^{\pi/2}= \pi