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\includegraphics[max width=\textwidth, alt={}, center]{77543862-ed95-42bf-b788-a9a43f039a89-4_995_905_260_621} The diagram shows parts of the curves \(y = ( 4 x + 1 ) ^ { \frac { 1 } { 2 } }\) and \(y = \frac { 1 } { 2 } x ^ { 2 } + 1\) intersecting at points \(P ( 0,1 )\) and \(Q ( 2,3 )\). The angle between the tangents to the two curves at \(Q\) is \(\alpha\).

1. Find \(\alpha\), giving your answer in degrees correct to 3 significant figures.
2. Find by integration the area of the shaded region.