OCR MEI C3 2014 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2014
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeTrigonometric integration
DifficultyModerate -0.8 This is a straightforward integration question requiring only basic techniques: integrating a constant and a sine function, then evaluating at simple limits. The only minor complication is the chain rule factor of 1/3 for sin 3x, but this is routine for C3 students. A 3-mark question testing standard integration skills with no problem-solving element makes it easier than average.
Spec1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)
Evaluate \(\int_0^{\frac{\pi}{4}} (1 - \sin 3x) \, dx\), giving your answer in exact form. [3]
AnswerMarks Guidance
\(\int_0^{\pi/6} (1 - \sin 3x) \, dx = \left[ x + \frac{1}{3}\cos 3x \right]_0^{\pi/6}\)M1 \(\pm 1/3 \cos 3x\) seen or \(\int \frac{1}{3}(1-\sin u) du\)
\(= \pi/6 - 1/3\)A1 cao condone \('+c'\); must be exact after correct answer seen
A1 cao [3]isw after correct answer seen 
$\int_0^{\pi/6} (1 - \sin 3x) \, dx = \left[ x + \frac{1}{3}\cos 3x \right]_0^{\pi/6}$ | M1 | $\pm 1/3 \cos 3x$ seen or $\int \frac{1}{3}(1-\sin u) du$ |
$= \pi/6 - 1/3$ | A1 cao | condone $'+c'$; must be exact after correct answer seen |
| A1 cao [3] | isw after correct answer seen |
Evaluate $\int_0^{\frac{\pi}{4}} (1 - \sin 3x) \, dx$, giving your answer in exact form. [3]

\hfill \mbox{\textit{OCR MEI C3 2014 Q1 [3]}}
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