The diagram shows the curve
\[\large y=e^{2x}-18x+15\]
The curve crosses the \(y\)-axis at \(P\) and the minimum point is at \(Q\). The shaded region is bounded by the curve and the line \(PQ\).

###### There are **3** marks available for part (i) and **8** marks for part (ii).

###### In total, this question is worth **15.3%** of all available marks in the paper.

###### This is part of the set OCR A Level Problems.

\((\text{i})\) Show that the \(x\)-coordinate of \(Q\) is \(\ln 3\).

\((\text{ii})\) Find the exact area of the shaded region.

**Input the nearest integer to \(100 \times\) the shaded area as your answer.**

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