The question is:
Let R be the region bounded between the x-axis and the curve $y=x^2-4x$. Find the volume generated by rotating R about the y-axis.
I used the shell method as the following
$\int_0^42\pi x(x^2-4x)dx$
$=2\pi\int_0^4(x^3-4x^2)$
$=2\pi[\frac14x^4-\frac43x^3]_0^4$
$=2\pi(64-256/3-0)$
$=-64\pi/3$
and got a negative value. Is there anything wrong in my steps?
https://www.youtube.com/watch?v=tcdakuqLBPE
This video had a similar question but had$y=4x-x^2$ instead of$y=x^2-4x$ and he got a positive value.