Given that
g(x)=4x2−13x+13x−3 g(x) = \frac{4x^2 - 13x + 13}{x - 3} g(x)=x−34x2−13x+13Write g(x)g(x)g(x) in the form
Ax+B+Cx−3 Ax + B + \frac{C}{x - 3} Ax+B+x−3Cwhere 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+βln3where α\alphaα and β\betaβ are integers to be found.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.