Volume of Gabriel's Horn/Corollary

Corollary to Volume of Gabriel's Horn
Consider Gabriel's horn, the solid of revolution formed by rotating about the $x$-axis the curve:


 * $y = \dfrac 1 x$

Consider the volume $V$ of the space enclosed by the plane $x = 1$ and the portion of Gabriel's horn where $x \ge 1$.

Then:
 * $V = \pi$