Linear mss density (mass/length) of a rod depends on the distanec from one end (say A) as `lamda_(x)=(alphax+beta)` here `alpha` and `beta` are constants, find the moment of inertia of this rod about an axis passing through `A` and perpendicular to the rod. Length of the rod is `l`.

Explanation

To find the moment of inertia of a rod with a linear mass density that varies with distance from one end, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Linear Mass Density**:
The linear mass density of the rod is given by:
\[
\lambda(x) = \alpha x + \beta
...