Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Let $I = \int_0^3 \frac{27}{\left(9 + x^2\right)^2}\,dx$.
(a)[4]

With the substitution $x = 3\tan\theta$, show that $I = \int_0^{\frac{1}{4}\pi} \cos^2\theta\, d\theta$.

(b)[4]

Hence determine the exact value of $I$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State, or make clear, that $dx = 3\sec^2\theta\,d\theta$” …

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