| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2011 |
| Session | June |
| Paper | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Use trig identity before definite integration |
| Difficulty | Challenging +1.8 This AEA question requires expanding the squared term, recognizing that tan²(x/2) = sec²(x/2) - 1, integrating sec²(x/2) using reverse chain rule, and handling tan(x/2) via substitution or recognition. While the techniques are standard, the multi-step algebraic manipulation and careful handling of limits with the half-angle makes this significantly harder than typical A-level integration, though not exceptionally difficult for AEA. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08h Integration by substitution |
Given that
$$\int_0^{\frac{\pi}{2}} (1 + \tan\left[\frac{1}{2}x\right])^2 \, dx = a + \ln b$$
find the value of $a$ and the value of $b$.
[Total 7 marks]
\hfill \mbox{\textit{Edexcel AEA 2011 Q2}}