(a(i))[3]
Show that $12\sin^2 x \cos^2 x$ is equal to $\frac{3}{2}(1 - \cos 4x)$.
(a(ii))[3]
Hence show that $\displaystyle \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} 12\sin^2 x \cos^2 x \, dx$ has value $\frac{\pi}{8} + $\frac{3\sqrt{3}}{16}$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $\sin 2x=2\sin x\cos x$ to turn the integrand into $k\sin^2 2x$” …
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