(i)[3]
By using the substitution $x = 2\sin\theta$, demonstrate that $I = \int_{0}^{\frac{1}{2}\pi} 4\sin^2\theta \, d\theta.$
(ii)[4]
Hence determine the exact value of $I.$
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Take $I = \int_{0}^{1} \frac{x^2}{\sqrt{(4 - x^2)}} \, dx.$
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State, or deduce, $\mathrm{d}x=2\cos\theta\,\mathrm{d}\theta$, or $\dfrac{\mathrm{d}x}{\mathrm{d}\theta}=2\cos\theta$” …
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