Let R be the region bounded by the curves
y=2x and x=4y-y^2
rotated around the x-axis
how do i set up the formula?
Did you draw a diagram?
Use the Shell Method here.
The required volume is given by:
$\displaystyle V = 2 \pi \int_0^{7/2} y \left( 4y - y^2 - \frac y2 \right)~dy$
Any questions?