OCR A Level: Core 3 - Differentiation and Integration [June 2013 Q9]

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 $PQ$ .

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

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

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Input the nearest integer to $100 \times$ the shaded area as your answer.

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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.

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This is part of the set OCR A Level Problems .