I am about to flip a shit: math

[Kirby]

this is literally the 3rd problem in my homework, I have spent over an hour on it

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x^4, y=1. about y=3

by every online guide, and my own book examples, the integral for it (I have to use the shell method for this) should be this:

2pi * the integral from 0 to 1: (3-y)(y^(1/4)) dy

but its not

what the hell am I doing wrong

[Kirby]

...

I needed both y^(1/4) and -y^(1/4) for the height

[trixie]

I am so done with math.