1.
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The diagram shows the curve with equation \(y = \ln ( 2 + \cos x ) , x \geq 0\).
The smallest value of \(x\) for which the curve meets the \(x\)-axis is \(a\) as shown.
- Find the value of \(a\).
- Use Simpson's rule with four strips of equal width to estimate the area of the region bounded by the curve in the interval \(0 \leq x \leq a\) and the coordinate axes.