OCR H240/03 2017 Specimen — Question 2 4 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2017
SessionSpecimen
Marks4
TopicNumerical integration
TypeTrapezium rule with stated number of strips
DifficultyEasy -1.2 This is a straightforward application of the trapezium rule with clearly specified parameters (4 strips, width 0.25). Part (a) requires only mechanical substitution into the trapezium rule formula with a simple function evaluation. Part (b) asks for standard textbook knowledge (use more strips). No problem-solving or conceptual insight required beyond basic recall and arithmetic.
Spec1.09f Trapezium rule: numerical integration

  1. Use the trapezium rule, with four strips each of width 0.25, to find an approximate value for \(\int_0^1 \frac{1}{\sqrt{1+x^2}} dx\). [3]
  2. Explain how the trapezium rule might be used to give a better approximation to the integral given in part (a). [1]

\begin{enumerate}[label=(\alph*)]
\item Use the trapezium rule, with four strips each of width 0.25, to find an approximate value for $\int_0^1 \frac{1}{\sqrt{1+x^2}} dx$. [3]

\item Explain how the trapezium rule might be used to give a better approximation to the integral given in part (a). [1]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2017 Q2 [4]}}