OCR A Level: Core 3 - Iteration [June 2007 Q6]

Calculus Level 3

\((\text{i})\) Given \(\displaystyle \int _{ 0 }^{ a }{ 6{ e }^{ 2x }+x } \, dx=42\), show that \[a=\dfrac{1}{2}\ln\left (15-\dfrac{a^2}{6}\right ).\]

\((\text{ii})\) Use an iterative formula to find \(a\), correct to 3 decimal places. Use a starting value of 1 and show the result of each iteration.

Input \(1000 \times\) your answer to part \((\text{ii})\).

There are 5 marks available for part (i) and 4 marks for part (ii).
In total, this question is worth 12.5% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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