Question $1$ Find the volume of the solid generated by revolving the region bounded by the curves $y= 2x$ , $y=x$ and $x=1$ around the $x-axis$.
Question $2$ Volume of the solid formed by rotating the region bounded by the curve, $y=3x^2$ and the lines $y=0$,$x=2$ around the $x-axis$ $?$
$V=2\pi \int_{x=0}^{1} \int_{y=x}^{2x}ydydx$ $=\pi \int_{x=0}^{1} 4x^2-x^2dx$ $=\pi$.
I believe this is correct for the first problem. Haven't done this in awhile. Second problem is different, but give it a try.