| 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 FP3 question requires recognizing that the integral splits into two parts: one yielding arcsin(2x) and another requiring substitution for the √(1-4x²) term. While the techniques are standard for Further Maths, the combination and algebraic manipulation needed elevate it slightly above average difficulty for A-level, though it remains a fairly routine FP3 exercise. |
| Spec | 1.08h Integration by substitution |
\begin{enumerate}[label=(\alph*)]
\item Find $\int \frac{1+x}{\sqrt{1-4x^2}} \, dx$. [5]
\item Find, to 3 decimal places, the value of
$$\int_0^{0.3} \frac{1+x}{\sqrt{1-4x^2}} \, dx.$$ [2]
\end{enumerate}
(Total 7 marks)
\hfill \mbox{\textit{Edexcel FP3 Q29 [7]}}