$($b$)(2$ mark$)$ Consider the solid generated by rotating the region on the right side of the line $x=\frac{b}{2}$ and restricted by the ellipse $\frac{x^2}{a^2}\frac{y^2}{b^2}=1.$ This region is rotated around $y-$axis, write the integral which represents the volume of the resulting solid. $($You do not need to evaluate the integral$).$