| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Partial fractions then inverse trig integration |
| Difficulty | Challenging +1.2 This is a standard Further Maths integration question requiring partial fractions decomposition of 1/(1-x^4) followed by routine inverse trig integration. While it involves multiple steps and Further Maths content, the techniques are well-practiced and the path is clear once partial fractions are set up. The 'show that' format adds minor difficulty but the answer form guides the solution. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08h Integration by substitution4.08c Improper integrals: infinite limits or discontinuous integrands |
5\\
Show that $\int _ { 0 } ^ { \frac { 1 } { \sqrt { 3 } } } \frac { 4 } { 1 - x ^ { 4 } } \mathrm {~d} x = \ln ( a + \sqrt { b } ) + \frac { \pi } { c }$ where $a , b$ and $c$ are integers to be determined.
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [6]}}