The diagram shows part of the curve \(y=x^2-7x+12\), cutting the \(x\)-axis at \(Q\). The normal to the curve at \(P(2,2)\) meets the \(x\)-axis at \(R\).
Show that the area of the shaded region bounded by the \(x\)-axis, the line \(PR\) and the curve is \(6\frac{5}{6}\) units\(^2\).[8]
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