Hello, kinana18!
Find the volume of the solid that results where the shaded region . Where?
is revolved about the yaxis. . $\displaystyle y\:=\:32x$
I'm not sure if you solve for x then integrate
or if you just integrate the equation as it is. I have no idea what you're talking about . . . do you?
The only region that makes any sense looks like this: Code:

3 *
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 +    *  
 1½
We have a right circular cone with $\displaystyle r = \tfrac{3}{2},\;h=3$
Its volume is: .$\displaystyle V \:=\:\tfrac{1}{3}\pi r^2h \:=\:\tfrac{1}{3}\pi\left(\tfrac{3}{2}\right)^2(3) \:=\:\frac{9\pi}{4}$
If we must use Calculus, I suggest Cylindrical Shells.
The formula is: .$\displaystyle V \;=\;2\pi\int^b_a\text{(radius)(height)}\,dx$
And we have: . $\displaystyle V \;=\;2\pi\int^{\frac{3}{2}}_0x(32x)\,dx $ . . . . etc.