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

Calculus Level 3

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.

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

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.

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