Computing the area of the region $$R = \lbrace (x,y)\,|\,x \ge 1, 0 \le y \le 1/x \rbrace$$ gives rise to the integral $$\int_1^\infty \frac {1}{x} dx$$ and it is not difficult to show that this integral diverges, so the area of the region is infinite

However, if the region $R$ is rotated about the x-axis, the result is a finite volume. Find this volume.

Volume =