Moderate -0.3 This is a straightforward application of linear interpolation formula using given interval endpoints. It requires evaluating f at two points and applying the standard formula, which is a routine FP1 technique with no conceptual challenges beyond careful arithmetic with trigonometric values.
$$f(x) = 2 \sin 2x + x - 2.$$
The root \(\alpha\) of the equation \(f(x) = 0\) lies in the interval \([2, \pi]\).
Using the end points of this interval find, by linear interpolation, an approximation to \(\alpha\).
[4]
$$f(x) = 2 \sin 2x + x - 2.$$
The root $\alpha$ of the equation $f(x) = 0$ lies in the interval $[2, \pi]$.
Using the end points of this interval find, by linear interpolation, an approximation to $\alpha$.
[4]
\hfill \mbox{\textit{Edexcel FP1 Q9 [4]}}