Math Help - volume rotated about y=2

Region bounded by y=x and y=x^2
find the volume when R is revolved about y=2

Does [a,b] = [0,2] or should I split the interval ---> [0,1] and [1,2]?

2. Originally Posted by Scottfranklin
Region bounded by y=x and y=x^2
find the volume when R is revolved about y=2

Does [a,b] = [0,2] or should I split the interval ---> [0,1] and [1,2]?
First find the points of intersection.

$x=x^2\Rightarrow{x=0,1}$

So we have

$V=\int_0^1[(2-x^2)^2-(2-x)^2]dx$