| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 10 |
| Topic | Integration by Substitution |
| Type | Indefinite integral with non-linear substitution (algebraic/exponential/logarithmic) |
| Difficulty | Challenging +1.3 This is a pure maths integration question (not mechanics despite the module name). Part (a) requires substitution u=x²+1 followed by polynomial integration - a standard technique but with multiple steps. Part (b) needs the identity tan²θ=sec²θ-1, then integration by parts for θsec²θ, requiring careful execution of several techniques. Both parts are moderately challenging multi-step problems requiring technique mastery beyond routine exercises, placing them above average difficulty. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
\begin{enumerate}[label=(\alph*)]
\item Find $\int 5x^3\sqrt{x^2 + 1} dx$. [5]
\item Find $\int \theta \tan^2 \theta d\theta$.
You may use the result $\int \tan \theta d\theta = \ln|\sec \theta| + c$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2017 Q7 [10]}}