| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Reduction Formulae |
| Type | Polynomial times trigonometric |
| Difficulty | Challenging +1.8 This is a challenging Further Maths reduction formula question requiring integration by parts twice to establish the recurrence relation, then recursive application to find I_6. The proof demands careful manipulation and the calculation involves multiple steps with powers of π/2, but follows a standard reduction formula template that FP3 students practice extensively. |
| Spec | 1.08i Integration by parts4.08a Maclaurin series: find series for function |
$$I_n = \int_0^{\frac{\pi}{2}} x^n \cos x \, dx, \quad n \geq 0.$$
\begin{enumerate}[label=(\alph*)]
\item Prove that $I_n = \left(\frac{\pi}{2}\right)^n - n(n-1)I_{n-2}$, $n \geq 2$. [5]
\item Find an exact expression for $I_6$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q4 [9]}}