Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Define $f(x)$ by $f(x) = \dfrac{-7x^2 + 2x - 6}{(1 + x)(4 + x)^2}$.
(a)[5]

Rewrite $f(x)$ in partial fractions.

(b)[6]

Hence calculate the exact value of $\int_0^2 f(x) \, dx$. Give your answer in the form $a\pi - \ln b$, where $a$ and $b$ are constants.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the form $\dfrac{A}{1+x}+\dfrac{Bx+C}{4+x^2}$” …

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