(a)[4]
Evaluate $\displaystyle \int_{1}^{\infty} \frac{1}{(3x - 2)^{\frac{3}{2}}}\,dx$.
(b)[4]
The diagram shows the curve with equation $y = \frac{1}{(3x - 2)^{\frac{3}{2}}}$. The shaded region is enclosed by the curve, the $x$-axis and the lines $x = 1$ and $x = 2$. The shaded region is turned through $360^\circ$ about the $x$-axis. Find the volume of revolution.
(c)[4]
The normal to the curve at the point $(1, 1)$ meets the $y$-axis at the point $A$. Find the $y$-coordinate of $A$.