| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2013 |
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| Session | June |
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| Topic | Integration by Parts |
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8
- Show that \(\int _ { 2 } ^ { 4 } 4 x \ln x \mathrm {~d} x = 56 \ln 2 - 12\).
- Use the substitution \(u = \sin 4 x\) to find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 24 } \pi } \cos ^ { 3 } 4 x \mathrm {~d} x\).