(i)[3]
With the substitution $x = 2\sin \theta$, show that $I = \int_0^{\tfrac{1}{6}\pi} 4\sin^2 \theta\,d\theta$.
(ii)[4]
Hence determine the exact value of $I$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $I = \int_0^1 \frac{x^2}{\sqrt{4 - x^2}}\,dx$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or imply $dx=2\cos\theta\,d\theta$, or $\frac{dx}{d\theta}=2\cos\theta$” …
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