1.5.6 Polynomials and rational expressions

Given that

\frac{4x^2 - 13x + 13}{x - 3}

a.

Write $g (x)$ in the form

\frac{C}{x - 3}

where $A$ , $B$ , and $C$ are integers to be found.

[4]

b.

Hence use algebraic integration to show that

\int_{4}^{6} g(x) \, dx = \alpha + \beta \ln 3

where $α\alpha$ and $b e t a$ are integers to be found.

[4]

Given that

\frac{4x^2 - 13x + 13}{x - 3}

a.

Write $g (x)$ in the form

\frac{C}{x - 3}

where $A$ , $B$ , and $C$ are integers to be found.

[4]

b.

Hence use algebraic integration to show that

\int_{4}^{6} g(x) \, dx = \alpha + \beta \ln 3

where $α\alpha$ and $b e t a$ are integers to be found.

[4]

1.5.6 Polynomials and rational expressions Questions