I am worried that my bounds are incorrect, so I am just making sure that my solution is valid
Let R be the region in the first quadrant bounded by the curve $y = (x − 2)^2$. Compute the volumes V1, V2, and V3 of the solids of revolution obtained by revolving R about the lines x = 0, x = 3, and y = −1, respectively.
For x = 0, aka y-axis, I decided to use the disk method and integrate wrt y.
I first found the bounds, from 0 to $y = (0-2)^2= 4$
and the final integral I came up with was
$$V = \int_0^4 \pi (\sqrt y + 2)^2 dy$$
and then I imagine that for x = 3 you simply subtract 3 from the original radius making it $\sqrt y + 5$.
My concern is with how I am setting up my boundaries and whether I should be changing the variable or not. Just making sure, thank you for any assistance!