I'm learning the disk method in integral calculus, and I'm having trouble understanding something that seems like it should be pretty basic.
For the curve $x^3$ rotated around $y=1$, I'm told that the radius of the disk is $r(x) = 1-x^3$
They give this diagram:
However, I thought a vertical translation of the curve would put it at $x^3-1$.
Wouldn't computing the curve this way change the problem? Can someone please help me understand this?