5. The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x ^ { - \frac { 1 } { 2 } }\), and the curve passes through the point \(( 4,5 )\). Find the equation of the curve. \section*{6.} The diagram shows the curve \(y = 4 - x ^ { 2 }\) and the line \(y = x + 2\).
\includegraphics[max width=\textwidth, alt={}, center]{6831b037-2ec7-499a-8bf6-62728a5681b7-2_408_435_27_1560}

1. Find the \(x\)-coordinates of the points of intersection of the curve and the line.
2. Use integration to find the area of the shaded region bounded by the line and the curve.