Mathematics 9709 · AS & A Level · Integration

Integration — practice question

(a)[3]

Find the quotient and remainder after dividing $18x^3 - 6x^2 - 30x + 4$ by $(3x - 1)$.

(b)[5]

Hence, find $\displaystyle \int_{1}^{5} \frac{18x^3 - 6x^2 - 30x + 4}{3x - 1}\,dx$ and express your answer as $a - \ln b$, where $a$ and $b$ are integers.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Carry out the division to at least the stage $6x^2+k_1$.

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