1. If c and d are the two values in the interval [0, 2] that divide the solid formed by revolving the region bounded by $y = x^2$, $y = 0$, $x = 1$ and $x = 2$ about the $x$-axis into three parts of equal volume, then $c^5 + d^5 = $\\
(a) 32\\
(b) $\frac{32}{3}$ \\
(c) $\frac{2\sqrt{2}}{3}$ \\
(d) $\frac{\sqrt[5]{2}}{3}$ \\
(e) $2\sqrt{2}$
