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Evaluate the integral:

$$\int_0^\frac\pi2 \sin^4\left(\dfrac x2\right)\cos^2\left(\dfrac x2\right) dx$$

A

$\dfrac{\pi-1}{32}$

B

$\dfrac{\pi}{16} - \dfrac{1}{8}$

C

$\dfrac{\pi}{16} - \dfrac{1}{32}$

D

$\dfrac{\pi}{32} - \dfrac{1}{24}$

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