| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Show substitution transforms integral, then apply integration by parts or further substitution |
| Difficulty | Standard +0.3 Part (a) is a standard substitution (u = x² + 1) requiring chain rule reversal and polynomial integration. Part (b) requires using the trig identity tan²θ = sec²θ - 1 followed by integration by parts, which is slightly more involved but still a routine A-level technique. Both parts are textbook-style exercises with clear pathways. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
7
\begin{enumerate}[label=(\alph*)]
\item Find $\int 5 x ^ { 3 } \sqrt { x ^ { 2 } + 1 } \mathrm {~d} x$.
\item Find $\int \theta \tan ^ { 2 } \theta \mathrm {~d} \theta$.
You may use the result $\int \tan \theta \mathrm { d } \theta = \ln | \sec \theta | + c$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 Q7 [10]}}