Mathematics 9709 · AS & A Level · Integration

Integration — practice question

Define $I = \int_{0}^{1} \frac{9}{(3 + x^2)^2}\,dx$.
(i)[3]

With the substitution $x = \sqrt{3}\tan\theta$, demonstrate that $I = \sqrt{3}\int_{0}^{\pi/6} \cos^2\theta \, d\theta$.

(ii)[4]

Hence determine the exact value of $I$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State, or infer, $dx = \sqrt{3}\sec^2\theta\,d\theta$” …

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