See the diagram below.

We proceed by the disk method:

V = int{A(x)}dx ................where A(x) represents the cross-sectional area of the circle obtained when rotating

...= int{pi*r^2}dx

...= int{pi*(2x^2)^2}dx

...= 4pi*int{x^4}dx from 0 up to 2

and we leave it there since they just asked us to express it, not evaluate it. knowing the disk method you could just jump to the last line, all the other lines were just there to kind of explain what i was doing.