| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Topic | Integration by Substitution |
| Type | Show definite integral equals specific value (algebraic/exponential substitution) |
| Difficulty | Standard +0.8 This is a moderately challenging integration problem requiring the insight to use an appropriate substitution (likely u = cos θ or u = 1 + cos θ) combined with simplifying sin 2θ = 2sin θ cos θ. While the techniques are standard A-level, finding the right approach and handling the logarithmic result requires solid problem-solving skills beyond routine exercises. The 7-mark allocation and 'show that' format confirm this is above-average difficulty. |
| Spec | 1.08h Integration by substitution |
Using an appropriate substitution, or otherwise, show that
$$\int_0^{\frac{\pi}{2}} \frac{\sin 2\theta}{1 + \cos \theta} d\theta = 2 - 2\ln 2$$ [7]
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q14 [7]}}