| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | September |
| Marks | 7 |
| Topic | Integration by Substitution |
| Type | Show definite integral equals specific value (trigonometric substitution or identity) |
| Difficulty | Standard +0.8 This is a definite integral requiring trigonometric manipulation (sin 2θ = 2sin θ cos θ) and substitution (likely u = 1 + cos θ), followed by integration of a rational function that produces a logarithm. While the techniques are standard Further Maths content, the multi-step algebraic manipulation and the specific target answer requiring ln 2 make it moderately challenging, above average difficulty but not exceptional. |
| Spec | 1.08h Integration by substitution |
Show that
$$\int_0^{\pi/2} \frac{\sin 2\theta}{1 + \cos \theta} \, d\theta = 2 - 2\ln 2$$
[7]
\hfill \mbox{\textit{SPS SPS FM 2020 Q9 [7]}}