In the rectangular coordinate plane, the shaded region between the curve $y = x ^ { 2 }$, the x-axis, and the line $x = 3$ is shown.
This shaded region is divided into three equal-area sub-regions by the lines $x = a$ and $x = b$.
Accordingly, what is the product $\mathbf { a } \cdot \mathbf { b }$?\\
A) $5 \sqrt { 2 }$\\
B) $4 \sqrt { 3 }$\\
C) $6 \sqrt { 3 }$\\
D) $3 \sqrt [ 3 ] { 6 }$\\
E) $2 \sqrt [ 3 ] { 9 }$