WJEC Unit 3 2023 June — Question 14 8 marks

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2023
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Parts
TypeIndependent multi-part (different techniques)
DifficultyModerate -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.
Spec1.08h Integration by substitution1.08i Integration by parts

  1. Use integration by parts to evaluate \(\int_0^1 (3x-1)e^{2x}\,dx\). [4]
  2. Use the substitution \(u = 1 - 2\cos x\) to find \(\int \frac{\sin x}{1 - 2\cos x}\,dx\). [4]

\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]}}