| Exam Board | Edexcel |
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| Module | AEA (Advanced Extension Award) |
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| Year | 2011 |
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| Session | June |
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| Topic | Standard Integrals and Reverse Chain Rule |
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2．Given that
$$\int _ { 0 } ^ { \frac { \pi } { 2 } } \left( 1 + \tan \left[ \frac { 1 } { 2 } x \right] \right) ^ { 2 } \mathrm {~d} x = a + \ln b$$
find the value of \(a\) and the value of \(b\) ．