| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Standard integral of 1/√(a²-x²) |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring completing the square (routine algebraic manipulation) followed by a standard inverse trig integral with substitution. While it involves Further Maths content, the techniques are mechanical and well-practiced, making it slightly easier than average overall but standard for FP2. |
| Spec | 4.08h Integration: inverse trig/hyperbolic substitutions |
6
\begin{enumerate}[label=(\alph*)]
\item Express $7 + 4 x - 2 x ^ { 2 }$ in the form $a - b ( x - c ) ^ { 2 }$, where $a , b$ and $c$ are integers.
\item By means of a suitable substitution, or otherwise, find the exact value of
$$\int _ { 1 } ^ { \frac { 5 } { 2 } } \frac { \mathrm {~d} x } { \sqrt { 7 + 4 x - 2 x ^ { 2 } } }$$
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2012 Q6 [8]}}