9709 P31 - Nov 2010 - Q5
1697
Let \(I = \int_0^1 \frac{x^2}{\sqrt{(4-x^2)}} \, dx\).
(i) Using the substitution \(x = 2 \sin \theta\), show that \(I = \int_0^{\frac{\pi}{6}} 4 \sin^2 \theta \, d\theta\).
(ii) Hence find the exact value of \(I\).
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