The diagram depicts a section of the curve $y = xe^{-x}$. The shaded region $R$ is enclosed by the curve together with the lines $x = 2$, $x = 3$ and $y = 0$.
(i)[3]
Apply the trapezium rule with two intervals to estimate the area of $R$, and give your answer correct to $2$ decimal places.
(ii)[1]
State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate of the actual area of $R$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give, or make clear, the correct ordinates $0.27067\ldots,\ 0.20521\ldots,\ 0.14936\ldots$” …