| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Completing square then standard inverse trig |
| Difficulty | Standard +0.8 This is a Further Maths FP3 question testing standard inverse trig/hyperbolic integration techniques. Part (a) requires completing the square and recognizing the inverse sinh form, while part (b) needs expressing sinh in exponential form or integration by parts. Both are textbook applications with straightforward execution, though the topic itself is advanced and requires careful algebraic manipulation. |
| Spec | 1.08i Integration by parts4.07d Differentiate/integrate: hyperbolic functions4.08h Integration: inverse trig/hyperbolic substitutions |
Using calculus, find the exact value of
\begin{enumerate}[label=(\alph*)]
\item $\int_1^2 \frac{1}{\sqrt{x^2 - 2x + 3}} \, dx$ [4]
\item $\int_0^1 e^{-x} \sinh x \, dx$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 2014 Q3 [8]}}