OCR MEI C3 — Question 4 4 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Parts
TypeBasic integration by parts
DifficultyStandard +0.3 This is a standard integration by parts question with a straightforward choice of u and dv. While it requires knowledge of the integration by parts formula and careful execution of the technique, it's a routine C3 exercise with no conceptual surprises—slightly easier than the typical multi-part C3 question but still requires proper technique.
Spec1.08i Integration by parts
Find \(\int x \sin 3x dx\). [4]
AnswerMarks Guidance
\(\int x\sin 3x \, dx\); \(u = x \Rightarrow \frac{du}{dx} = 1\), \(\frac{dv}{dx} = \sin 3x \Rightarrow v = -\frac{1}{3}\cos x\)M1
\(= -\frac{1}{3}x\cos 3x + \int \frac{1}{3}\cos 3x \, dx\)A1, M1
\(= -\frac{1}{3}x\cos 3x + \frac{1}{9}\sin 3x + c\)A1 Choice of \(u\); Correct form \(-\frac{1}{3}\cos 3x\); Correct form; \(c\) must be seen. 4 marks 
$\int x\sin 3x \, dx$; $u = x \Rightarrow \frac{du}{dx} = 1$, $\frac{dv}{dx} = \sin 3x \Rightarrow v = -\frac{1}{3}\cos x$ | M1

$= -\frac{1}{3}x\cos 3x + \int \frac{1}{3}\cos 3x \, dx$ | A1, M1

$= -\frac{1}{3}x\cos 3x + \frac{1}{9}\sin 3x + c$ | A1 | Choice of $u$; Correct form $-\frac{1}{3}\cos 3x$; Correct form; $c$ must be seen. 4 marks

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Find $\int x \sin 3x dx$. [4]

\hfill \mbox{\textit{OCR MEI C3  Q4 [4]}}
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Q1 5 Q2 4 Q3 6 Q4 4 Q5 4 Q6 7 Q7 6 Q8 18 Q9 18