$2$: Let $R$ be the region bounded by the graph $y=\sqrt[\phantom{2}]{x},x=0,y=2.$ Let $E$ be the solid generated by remolyng: R about the line $y=0.$ Set up $($but do not evaluate$)$ an lategrat to find the volume of the solid $E$ by the following steps with the shell method:

a: Sketch the region $R.$

be Determine the direction$/$orientation of the cylindrical sheel and then determine whether we are saing $dx$ or dy for the thickness.

et What is the expressice of the surface area of the glindrical shell in terms of a asil$/$or $8"($This depends on your answer of the previous question$)$

di Set up the integral to calculate the volume of the solid. $($Do not need to evaluate the integral$)$