SPS SPS SM Pure 2021 May — Question 2 4 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionMay
Marks4
TopicNumerical integration
TypeTrapezium rule with stated number of strips
DifficultyModerate -0.8 This is a straightforward application of the trapezium rule with clearly specified parameters (4 strips, width 0.5). Part (a) requires only mechanical substitution into the trapezium rule formula with no conceptual difficulty. Part (b) asks for standard textbook knowledge (use more strips). The question is easier than average as it involves direct application of a numerical method with no problem-solving or insight required.
Spec1.09f Trapezium rule: numerical integration

  1. Use the trapezium rule, with four strips each of width \(0.5\), to estimate the value of $$\int_0^2 e^{x^2} dx$$ giving your answer correct to 3 significant figures. [3]
  2. Explain how the trapezium rule could be used to obtain a more accurate estimate. [1]

\begin{enumerate}[label=(\alph*)]
\item Use the trapezium rule, with four strips each of width $0.5$, to estimate the value of
$$\int_0^2 e^{x^2} dx$$
giving your answer correct to 3 significant figures. [3]

\item Explain how the trapezium rule could be used to obtain a more accurate estimate. [1]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q2 [4]}}