Disk/Washer and Shell Methods
1. Find the volume of the solid obtained by rotating
the region bounded by \( y=x^3, y=8\) and the y-axis about the y-axis.
2. Find the volume of
the solid generated by rotating the region enclosed by the curves \(y=x\)
and \(y=x^2\) about the y-axis.
3. Find the volume of the solid generated by revolving the region
bounded by the curves \(y=\sqrt{x}, x=4\) and \(y=0\) about the
line \(y=-2\).
4. Find the volume of the solid obtained by rotating about the line \(x=-2\),
the region bounded by \(y=x\) and \(y=x^2\).