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\includegraphics[max width=\textwidth, alt={}, center]{77f27b11-b931-481f-b4ef-5e549eff8086-14_631_689_274_721}
The diagram shows part of the curve with equation \(y = \frac { 4 } { ( 2 x - 1 ) ^ { 2 } }\) and parts of the lines \(x = 1\) and \(y = 1\). The curve passes through the points \(A ( 1,4 )\) and \(B , \left( \frac { 3 } { 2 } , 1 \right)\).
- Find the exact volume generated when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
- 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.