OCR C2 2010 June — Question 2 5 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2010
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNumerical integration
TypeTrapezium rule accuracy improvement explanation
DifficultyModerate -0.8 This is a straightforward application of the trapezium rule with clearly specified parameters (3 strips, width 3). Part (i) requires only substitution into the standard formula with simple cube root evaluations. Part (ii) tests basic understanding that more strips improve accuracy—a standard bookwork response. No problem-solving or conceptual challenge beyond routine procedure.
Spec1.09f Trapezium rule: numerical integration

2
  1. Use the trapezium rule, with 3 strips each of width 3 , to estimate the area of the region bounded by the curve \(y = \sqrt [ 3 ] { 7 + x }\), the \(x\)-axis, and the lines \(x = 1\) and \(x = 10\). Give your answer correct to 3 significant figures.
  2. Explain how the trapezium rule could be used to obtain a more accurate estimate of the area.

2 (i) Use the trapezium rule, with 3 strips each of width 3 , to estimate the area of the region bounded by the curve $y = \sqrt [ 3 ] { 7 + x }$, the $x$-axis, and the lines $x = 1$ and $x = 10$. Give your answer correct to 3 significant figures.\\
(ii) Explain how the trapezium rule could be used to obtain a more accurate estimate of the area.

\hfill \mbox{\textit{OCR C2 2010 Q2 [5]}}