| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Standard integral of 1/(a²+x²) |
| Difficulty | Standard +0.8 This is a Further Maths question requiring completing the square followed by recognition and application of the inverse tangent integration formula. Part (a) is routine algebraic manipulation (3 marks), while part (b) requires knowing the standard result ∫1/(x²+a²)dx = (1/a)arctan(x/a) + c and careful substitution with exact arithmetic. The topic itself (inverse trig integration) is beyond standard A-level, and the multi-step nature with exact values pushes this above average difficulty, though it remains a fairly standard FP3 exercise rather than requiring deep insight. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.08h Integration by substitution |
$$4x^2 + 4x + 17 \equiv (ax + b)^2 + c, \quad a > 0.$$
\begin{enumerate}[label=(\alph*)]
\item Find the values of $a$, $b$ and $c$. [3]
\item Find the exact value of
$$\int_{-0.5}^{1.5} \frac{1}{4x^2 + 4x + 17} \, dx.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q22 [7]}}