Find the volume of the solid generated by revolving the regi

Find the volume of the solid generated by revolving the region bounded by the curves y = (x - 2)^2 and y = 1 around the y-axis.

Solution

y=x,x=0,y=2y=x,x=0,y=2 around the Y-axis.

I can\'t seem to get the setup right. I know the formula for cylindrical shell is 2rht2rht my problem is that I\'m not getting the right answer (88) I thought the setup would be

2xxdx2xxdx

but I keep getting it wrong. I think the upper bound is 4 and the lower bound is 0 (since square root 4 is 2 which is where y is) I\'m not even sure that I should be taking x for the radius since x=0. any help would be greatly appreciated.