Find the volume of the solid generated by revolving the bounded region about the $y-$axis.

$y=8sin(x^2),x=0,x=\sqrt[\phantom{2}]{\frac{}{2}},y=8$

units ${?}^3$

Tutorial

The Cylindrical shell method to find the solid obtained by rotating the region between two functions $f(x)$ and $g(x)$ satisfyin above, from below, from the left, and from the right? Remember to use u$-$substitution appropriately in the integration.

Additional Materials

Reading

$9.$ Points$]$

OSCALC$16\mathrm{.}3\mathrm{.}148.$

Find the volume $($in units ${?}^3)$ generated when the region between the curves is rotated around the given axis:

$x=y^2$ and $y=x$ rotated around the line $y=6$

units ${?}^3$