6.
\includegraphics[max width=\textwidth, alt={}, center]{38c285f8-a542-42fb-aa4c-41adb9a8f63e-2_503_839_1208_557} The diagram shows the curve with equation \(y = 4 x ^ { \frac { 1 } { 3 } } - x , x \geq 0\).
The curve meets the \(x\)-axis at the origin and at the point \(A\) with coordinates \(( a , 0 )\).

1. Show that \(a = 8\).
2. Find the area of the finite region bounded by the curve and the positive \(x\)-axis.