# What is the volume of the solid generated by revolving the region bounded by y=sqrt(sin6x), y=0, and the x-axis, if 0<=x<=pi/6?

$V = {\int}_{0}^{\frac{\pi}{6}} \pi \cdot {\left(\sqrt{\sin \left(6 x\right)}\right)}^{2} \mathrm{dx} = \frac{\pi}{3}$