Find the exact volume of the solid obtained by rotating the region bounded by the curve $\displaystyle {y}={\sin{{\left({6}{x}^{{2}}\right)}}}$ and the $\displaystyle {x}$-axis, from $\displaystyle {x}={0}$ to $\displaystyle {x}=\sqrt{{{\frac{{\pi}}{{{6}}}}}}$, about the $\displaystyle {y}$-axis.

$\displaystyle {V}=$ Preview Question 6