11
\includegraphics[max width=\textwidth, alt={}, center]{10b2ec29-adca-4313-ae24-bab8b2d9f8a4-16_505_1166_258_486}
The diagram shows the line \(x = \frac { 5 } { 2 }\), part of the curve \(y = \frac { 1 } { 2 } x + \frac { 7 } { 10 } - \frac { 1 } { ( x - 2 ) ^ { \frac { 1 } { 3 } } }\) and the normal to the curve at the point \(A \left( 3 , \frac { 6 } { 5 } \right)\).
- Find the \(x\)-coordinate of the point where the normal to the curve meets the \(x\)-axis.
- Find the area of the shaded region, giving your answer correct to 2 decimal places.