| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Integration using reciprocal identities |
| Difficulty | Standard +0.3 This is a straightforward application of the identity cot²(2x) = cosec²(2x) - 1, followed by direct integration using standard results. It requires recall of one reciprocal identity and knowledge that ∫cosec²(u)du = -cot(u), with a simple chain rule adjustment for the factor of 2. This is slightly easier than average as it's a standard textbook exercise with a clear method. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\int (\operatorname{cosec}^2 2x - 1) dx\) | M1 A1 | |
| \(= -\frac{1}{2} \cot 2x - x + c\) | M1 A1 | (4) |
$\int (\operatorname{cosec}^2 2x - 1) dx$ | M1 A1 |
$= -\frac{1}{2} \cot 2x - x + c$ | M1 A1 | (4)\begin{enumerate}
\item Find
\end{enumerate}
$$\int \cot ^ { 2 } 2 x \mathrm {~d} x$$
\hfill \mbox{\textit{Edexcel C4 Q1 [4]}}