| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Moderate -0.3 Both parts are standard textbook exercises testing routine techniques. Part (a) is straightforward integration by parts with polynomial and exponential—a classic example. Part (b) is a direct substitution where du/dx is visible in the numerator. Neither requires problem-solving insight, just mechanical application of learned methods, making this slightly easier than average. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
\begin{enumerate}[label=(\alph*)]
\item Use integration by parts to evaluate $\int_0^1 (3x-1)e^{2x}\,dx$. [4]
\item Use the substitution $u = 1 - 2\cos x$ to find $\int \frac{\sin x}{1 - 2\cos x}\,dx$. [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q14 [8]}}