OCR A Level: Core 4 - Partial Fractions [January 2013 Q10]

$(\text{i})$ Use algebraic division to express $\dfrac{x^3-2x^2-4x+13}{x^2-x-6}$ in the form $Ax+B+\dfrac{Cx+D}{x^2-x-6}$ , where $A$ , $B$ , $C$ and $D$ are constants.

$(\text{ii})$ Hence find $\large \int _{ 4 }^{ 6 }{ \frac { x^{ 3 }-2x^{ 2 }-4x+13 }{ x^{ 2 }-x-6 } } \, dx$ giving your answer in the form $a+ \ln b$ .

---

Input $ab$ as your answer.

---

There are 4 marks available for part (i) and 7 marks for part (ii).

In total, this question is worth 15.3% of all available marks in the paper.

---

This is part of the set OCR A Level Problems .