By the washer method I can integrate the following function fine,

x = y²

x = 4

y = 0

about the y-axis.

V = ∫π(4² - (y²)²)dy [0,2]

but if I use the shell method this is how I set it up:

V = ∫2πy(4² - y²)dy [0,2]

but I get an incorrect answer.

By the washer method I get (128π)/5 but by the shell method I get 8π.

I just need to set it up correctly, I'd really appreciate it.