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
DifficultyModerate -0.3 This is a straightforward integration by parts question with a simple exponential function. It requires only one application of the standard technique with no complications, making it slightly easier than average for A-level but still requiring proper execution of the method.
Spec1.08i Integration by parts
Find \(\int xe^{3x} \, dx\). [4]
AnswerMarks Guidance
Answer/Working: Let \(u = x\), \(du/dx = e^x \Rightarrow v = e^{x/3}\); \(\int xe^x dx = \frac{1}{3}xe^x - \int \frac{1}{3}e^x dx = \frac{1}{3}xe^x - \frac{1}{9}e^x + c\)M1, A1, A1, B1, [4] parts with \(u = x\), \(du/dx = e^x \Rightarrow v\); \(= \frac{1}{3}xe^x - \frac{1}{9}e^x\) +c 
**Answer/Working:** Let $u = x$, $du/dx = e^x \Rightarrow v = e^{x/3}$; $\int xe^x dx = \frac{1}{3}xe^x - \int \frac{1}{3}e^x dx = \frac{1}{3}xe^x - \frac{1}{9}e^x + c$ | **M1, A1, A1, B1, [4]** | parts with $u = x$, $du/dx = e^x \Rightarrow v$; $= \frac{1}{3}xe^x - \frac{1}{9}e^x$ +c

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Find $\int xe^{3x} \, dx$. [4]

\hfill \mbox{\textit{OCR MEI C3  Q4 [4]}}
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Q1 5 Q2 18 Q3 19 Q4 4 Q5 4