| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Standard +0.3 Part (i) is a standard integration by parts exercise with a polynomial and logarithm—textbook routine for C4. Part (ii) requires a trigonometric substitution and simplification using identities, which is more involved but still a well-practiced technique. Both parts are typical C4 exam questions requiring methodical application of learned techniques rather than novel problem-solving, placing this slightly above average difficulty. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
\begin{enumerate}[label=(\roman*)]
\item Use integration by parts to find the exact value of $\int_1^3 x^2 \ln x \, dx$. [6]
\item Use the substitution $x = \sin \theta$ to show that, for $|x| \leq 1$,
$$\int \frac{1}{(1 - x^2)^{\frac{3}{2}}} \, dx = \frac{x}{(1 - x^2)^{\frac{1}{2}}} + c, \text{ where } c \text{ is an arbitrary constant.}$$ [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q14 [12]}}