Moderate -0.5 This question combines two routine techniques: applying the trapezium rule (a standard numerical method) and handling absolute values by identifying where the function changes sign (2^x = 8 when x = 3). While it requires careful evaluation at multiple points and understanding of absolute values, both components are standard A-level procedures with no novel problem-solving required. The four-interval trapezium rule is straightforward bookwork, making this slightly easier than average.
1 Use the trapezium rule with four intervals to find an approximation to
$$\int _ { 1 } ^ { 5 } \left| 2 ^ { x } - 8 \right| \mathrm { d } x$$
\hfill \mbox{\textit{CAIE P2 2014 Q1 [3]}}