# 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 $$(\text{ii})$$.

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