| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2002 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Integration of e^(ax)·trig(bx) |
| Difficulty | Challenging +1.2 This is a standard integration by parts problem requiring two applications to create a system of equations relating S and C. While it requires careful algebraic manipulation and evaluation at limits, the technique is well-established and taught explicitly in Further Maths. The AEA context adds slight difficulty, but this is a textbook example of the e^(ax)·trig(bx) type rather than requiring novel insight. |
| Spec | 1.08i Integration by parts |
2.Given that $S = \int _ { 0 } ^ { \frac { \pi } { 2 } } \mathrm { e } ^ { 2 x } \sin x \mathrm {~d} x$ and $C = \int _ { 0 } ^ { \frac { \pi } { 2 } } \mathrm { e } ^ { 2 x } \cos x \mathrm {~d} x$ ,
\begin{enumerate}[label=(\alph*)]
\item show that $S = 1 + 2 C$ ,
\item find the exact value of $S$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2002 Q2 [9]}}