Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}(\sin4x-4x)=-8\sin^22x$.[3] Hence evaluate the exac

Question

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}(\sin4x-4x)=-8\sin^22x$.[3] Hence evaluate the exact value of $\displaystyle\int_0^{\pi/8}\sin^22x\,\mathrm{d}x$.[3]

Accepted Answer

$\dfrac{\pi-2}{16}$

Squared-sine integral from a derivative identity

Squared-sine integral from a derivative identity

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