Problem

The diagram shows part of the curve with equation $y=\frac{4}{(2x-1)^2}$ and parts of the lines $x=1$ and $y=1$.

The curve passes through the points $A(1,4)$ and $B\left(\frac{3}{2},1\right)$.

(a) Find the exact volume generated when the shaded region is rotated through $360^\circ$ about the $x$-axis.

(b) A triangle is formed from the tangent to the curve at $B$, the normal to the curve at $B$ and the $x$-axis.

Find the area of this triangle.