| Exam Board | OCR |
|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
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| Session | Specimen |
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| Topic | Integration by Parts |
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5 In this question you must show detailed reasoning.
Evaluate \(\int _ { 0 } ^ { \infty } 2 x \mathrm { e } ^ { - x } \mathrm {~d} x\).
[0pt]
[You may use the result \(\lim _ { x \rightarrow \infty } x \mathrm { e } ^ { - x } = 0\).]