| Exam Board | OCR |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Year | 2009 |
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| Session | June |
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| Topic | Integration using inverse trig and hyperbolic functions |
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6 Given that
$$\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { 16 + 9 x ^ { 2 } } } \mathrm {~d} x + \int _ { 0 } ^ { 2 } \frac { 1 } { \sqrt { 9 + 4 x ^ { 2 } } } \mathrm {~d} x = \ln a$$
find the exact value of \(a\).