(i)[4]
With the substitution $x = \cos^2 \theta$, establish that $I = \displaystyle\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} 2\cos^2 \theta\, d\theta$.
(ii)[4]
Therefore determine the exact value of $I$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Take $I = \displaystyle\int_{\frac{1}{4}}^{\frac{3}{4}} \sqrt{\dfrac{x}{1 - x}}\, dx$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write down or infer $dx=-2\cos\theta\sin\theta\,d\theta$, or an equivalent form” …
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