(a)[5]
Express $f(x)$ as partial fractions.
(b)[5]
Hence find the exact value of $\int_{-a}^{a} f(x)\, dx$, and present your answer in the form $p \ln q + r \ln s$ where $p$ and $r$ are integers and $q$ and $s$ are prime numbers.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Take $f(x) = \dfrac{36a^2}{(2a + x)(2a - x)(5a - 2x)}$, where $a$ is a positive constant.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the partial fraction decomposition $\dfrac{A}{2a+x}+\dfrac{B}{2a-x}+\dfrac{C}{5a-2x}$.” …
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