Problem

Figure 1 shows a sketch of part of the curve with equation

$$y=\frac{9}{(2x-3)^{1.25}}\qquad x>\frac{3}{2}$$

The finite region $R$, shown shaded in Figure 1, is bounded by the curve, the line with equation $y=9$ and the line with equation $x=6$

This region is rotated through $2\pi$ radians about the $x$-axis to form a solid of revolution.

Find, by algebraic integration, the exact volume of the solid generated.