5 The curve with equation \(y = 16 - x ^ { 4 }\) is sketched below.
\includegraphics[max width=\textwidth, alt={}, center]{fddf5016-a5bd-42db-b5c4-f4980b8d9d67-3_435_663_824_685}
The points \(A ( - 2,0 ) , B ( 2,0 )\) and \(C ( 1,15 )\) lie on the curve.
- Find an equation of the straight line \(A C\).
- Find \(\int _ { - 2 } ^ { 1 } \left( 16 - x ^ { 4 } \right) \mathrm { d } x\).
- Hence calculate the area of the shaded region bounded by the curve and the line \(A C\).