Question:

$\int_{0}^{\pi/2} \sin^4 2x \, dx = \int_{0}^{\pi/2} (2 \sin x \cos x)^4 \, dx = 16 \int_{0}^{\pi/2} \sin^4 x \cdot \cos^4 x \, dx$<br>Using Walli's Theorem for $m = 4, n = 4$ (both even):<br>$I = 16 \left[ \frac{(3 \cdot 1) \cdot (3 \cdot 1)}{8 \cdot 6 \cdot 4 \cdot 2} \cdot \frac{\pi}{2} \right] = 16 \cdot \frac{9}{384} \cdot \frac{\pi}{2} = \frac{3\pi}{16}$