1. Find the area between the following curves.
f(x) = -8x\textsuperscript{2} + 8x, g(x) = x - \sqrt{x}
2. Find the volume obtained by rotating the region enclosed by the following curves about the
specified line
y = 4(x\textsuperscript{2} + 4), y = 4(12 - x\textsuperscript{2}) about y = -4
3. Find the volume of the solid obtained by rotating the region bounded by x = y\textsuperscript{2} and
x = 2y about the y-axis.
4. Use the method of cylindrical shells to find the volume of the solid generated by
revolving the region bounded by the graphs of the equations about the indicated axis.
Sketch the region and a representative rectangle.
y = x\textsuperscript{2}, y = 0, x = 3; the y-axis
