| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Indefinite integral with non-linear substitution (algebraic/exponential/logarithmic) |
| Difficulty | Standard +0.8 This is a substitution-based integration requiring students to find du/dx = 2sec²x, recognize that 1/cos²x = sec²x, and simplify the integral to ∫(1/2u²)du. While the substitution is given, students must correctly handle the relationship between sec²x and the substitution, then integrate and back-substitute. This requires more insight than routine C3 integration but is a standard exam technique, placing it moderately above average difficulty. |
| Spec | 1.08h Integration by substitution |
Use the substitution $u = 1 + 2\tan x$ to find
$$\int \frac{1}{(1 + 2\tan x)^2 \cos^2 x} \, dx$$ [5]
\hfill \mbox{\textit{AQA C3 2011 Q8 [5]}}