Given that g(x)=4x2−13x+13x−3g(x) = \frac{4x^2 - 13x + 13}{x - 3}g(x)=x−34x2−13x+13
Write g(x)g(x)g(x) in the form Ax+B+Cx−3Ax + B + \frac{C}{x - 3}Ax+B+x−3C where AAA, BBB, and CCC are integers to be found.
Hence use algebraic integration to show that ∫46g(x) dx=α+βln3\int_{4}^{6} g(x) \, dx = \alpha + \beta \ln 3∫46g(x)dx=α+βln3 where α\alphaα and betabetabeta are integers to be found.
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.