\pi\int_0^2 [ (8)^2 - (8 - 2x^2)^2 ] \,dx
I think that works, because if you use the washer method, the outer radius is just the part that has a y-length of 8, and the inner radius is the part above the function and under y=8, so using pi (R^2 - r^2) integrated, that's what I get. Hope that...