June 2022 Paper 3 Q2

2 The shaded region, shown in the diagram below, is defined by

\[x^2 - 7x + 7 \leqslant y \leqslant 7 - 2x\]

Identify which of the following gives the area of the shaded region.

Tick (✓) one box. [1 mark]

• \(\displaystyle\int (7 - 2x)\,\mathrm{d}x - \int (x^2 - 7x + 7)\,\mathrm{d}x\)
• \(\displaystyle\int_0^5 (x^2 - 5x)\,\mathrm{d}x\)
• \(\displaystyle\int_0^5 (5x - x^2)\,\mathrm{d}x\)
• \(\displaystyle\int_0^5 (x^2 - 9x + 14)\,\mathrm{d}x\)