Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Define $f(x) = \dfrac{4x^2 + 9x - 8}{(x + 2)(2x - 1)}$.

(i)[4]

Write $f(x)$ in the form $A + \dfrac{B}{x + 2} + \dfrac{C}{2x - 1}$.

(ii)[5]

Hence prove that $\int_{1}^{4} f(x)\,dx = 6 + \frac{1}{2}\ln\left(\frac{16}{7}\right)$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply a suitable method to find one constant” …