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

Calculus Level 4

\((\text{i})\) 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.

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