Trapezium rule with reasoning

A question is this type if and only if it asks to use the trapezium rule AND requires explanation of whether the result is an overestimate or underestimate, or how to improve accuracy.

2 questions · Easy -1.1

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CAIE P2 2016 November Q5
8 marks Moderate -0.3
\includegraphics{figure_5} The diagram shows the curve \(y = \sqrt{1 + e^{4x}}\) for \(0 \leq x \leq 6\). The region bounded by the curve and the lines \(x = 0\), \(x = 6\) and \(y = 0\) is denoted by \(R\).
  1. Use the trapezium rule with 2 strips to find an estimate of the area of \(R\), giving your answer correct to 2 decimal places. [3]
  2. With reference to the diagram, explain why this estimate is greater than the exact area of \(R\). [1]
  3. The region \(R\) is rotated completely about the \(x\)-axis. Find the exact volume of the solid produced. [4]
AQA Paper 3 2023 June Q2
1 marks Easy -1.8
The trapezium rule is used to estimate the area of the shaded region in each of the graphs below. Identify the graph for which the trapezium rule produces an overestimate. Tick (\(\checkmark\)) one box. [1 mark] \includegraphics{figure_2}