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The linear mass density of a thin rod AB of length L varies from A to B as $\lambda(x) = \lambda_0\left(1 + \frac{x}{L}\right)$, where $x$ is the distance from A. If $M$ is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:
(1) $\frac{5}{12}ML^2$
(2) $\frac{7}{18}ML^2$
(3) $\frac{2}{5}ML^2$
(4) $\frac{3}{7}ML^2$
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