| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Standard +0.3 Part (i) is a standard integration by parts application with exponential function. Part (ii) is routine integration by substitution or recognition. Part (iii) is a separable differential equation requiring trigonometric manipulation and integration, which is more challenging but still follows standard C4 techniques. Overall slightly above average difficulty due to the multi-step trigonometric work in part (iii), but all parts use well-practiced methods. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08i Integration by parts1.08k Separable differential equations: dy/dx = f(x)g(y) |
\begin{enumerate}
\item[(i)] Find
$$\int xe^{4x} dx$$ \hfill [3]
\item[(ii)] Find
$$\int \frac{8}{(2x - 1)^3} dx, \quad x > \frac{1}{2}$$ \hfill [2]
\item[(iii)] Given that $y = \frac{\pi}{6}$ at $x = 0$, solve the differential equation
$$\frac{dy}{dx} = e^x \cosec 2y \cosec y$$ \hfill [7]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2014 Q6 [12]}}