1.80: Area between a parabola and a line

0606/13/O/N/18 — Question 10 · 9 marks

1.80 diagram
The diagram shows the curve y=12+x−x2y = 12 + x - x^{2} intersecting the line y=x+8y = x + 8 at the points AA and BB.
(i)
Find the coordinates of the points AA and BB.
[3]
(ii)
Find ∫(12+x−x2) dx\displaystyle\int (12 + x - x^{2})\,\mathrm{d}x.
[2]
(iii)
Showing all your working, find the area of the shaded region.
[4]