The moment of inertia and the position of the axis

A uniform rod of mass $1.8\ \text{kg}$ and length $1.2\ \text{m}$ can turn about an axis at right angles to it, anywhere along it. You will make the program find its moment of inertia for every position of the axis, check one value by adding up small pieces, and find where it doubles.

The idea. About the middle, $I_{cm} = \dfrac{ML^2}{12}$. The parallel axis theorem moves the axis by $d$: $I = I_{cm} + Md^2$.

Your tasks.

1. Work out I for every distance d of the axis from the middle.
2. Find I about one end by cutting the rod into $2000$ small pieces and adding $m r^2$ for each.
3. Find the d in the list where I is closest to twice its smallest value.