Answer
$$\dfrac{\pi^2}{16} $$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume = \int_{0}^{\pi/2} (\dfrac{\pi}{4}) \sin^2 (2x) dx \\=(\dfrac{\pi}{4}) \int_{0}^{\pi/2} (1- \cos 4x) \space dx \\=(\dfrac{\pi}{8}) \dfrac{\pi}{2}- (\dfrac{\pi}{8}) \cdot \dfrac{\sin (2 \pi) }{4}-(\dfrac{\pi}{8}) (0)+(\dfrac{\pi}{8}) (0)] \space dy \\= (\dfrac{\pi}{8})[\dfrac{\pi}{2}-0] \\=\dfrac{\pi^2}{16} $$
