Calculating Volumes via Disks or Washers

We define Gabriel's Modified Horn as the shape generated when we revolve the graph of $y = \frac{1}{x^{\alpha}}$ around the $x$-axis for $x \geq 1,$ where $\alpha > \frac{1}{2}$ is a parameter. What is the asymptotic order of the volume of Gabriel's Horn in terms of $\alpha$?