OCR MEI C2 2010 June — Question 5 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2010
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypePure definite integration
DifficultyModerate -0.8 This is a straightforward integration question requiring only basic power rule application (rewriting 1/x³ as x⁻³) and evaluation of definite integral limits. It's simpler than average A-level questions as it involves direct application of a single technique with no problem-solving or conceptual challenges, though the negative power and fraction coefficient require careful arithmetic.
Spec1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits
Find \(\int_{2}^{5} \left(1 - \frac{6}{x^3}\right) dx\). [4]
AnswerMarks Guidance
\(x = \frac{6x^{-2}}{-2}\) o.e.2 marks M1 for 1 term correct
Their \([5 + \frac{3}{2x}] - [2 + \frac{3}{4}]\)M1 Dependent on at least M1 already earned
\(= 2.37\) o.e. c.a.o.A1 i.s.w. 
$x = \frac{6x^{-2}}{-2}$ o.e. | 2 marks | M1 for 1 term correct
Their $[5 + \frac{3}{2x}] - [2 + \frac{3}{4}]$ | M1 | Dependent on at least M1 already earned
$= 2.37$ o.e. c.a.o. | A1 | i.s.w.
Find $\int_{2}^{5} \left(1 - \frac{6}{x^3}\right) dx$. [4]

\hfill \mbox{\textit{OCR MEI C2 2010 Q5 [4]}}
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