| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Integration using chain rule reversal |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing algebraic manipulation and basic integration. Part (a) requires simple equation solving, part (b) is routine expansion of brackets, and part (c) applies the fundamental theorem of calculus with standard power rule integration. All techniques are standard C2 level with no novel insight required, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
Given that $f'(x) = (2x^3 - 3x^{-2})^2 + 5$, $x > 0$,
\begin{enumerate}[label=(\alph*)]
\item Find, to 3 significant figures, the value of $x$ for which $f'(x) = 5$. [3]
\item Show that $f'(x)$ may be written in the form $Ax^6 + \frac{B}{x^4} + C$, where $A$, $B$ and $C$ are constants to be found. [3]
\item Hence evaluate $\int_1^2 f'(x) \, dx$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q25 [11]}}