Regions in cylindrical coordinates

As its name suggests, this coordinate system is good for regions shaped like cylinders or pieces of cylinders.

1.

Let W be the cylinder of radius 4 centered on the z-axis between z = -1 and z = 3.

Thus, W is described by $0 \le r \le 4, 0 \le \theta \le 2\pi, -1 \le z \le 3$.

2.

Let W be the region between the cylinders of radius 2 and 3, bounded by the xy-plane, the plane z = 1, the plane x = 0 and the plane y = 0. Thus, W is described by $2 \le r \le 3, 0 \le \theta \le \frac{\pi}{2}, 0 \le z \le 1$.