The linear density of a thin rod of length 1m lies as `lambda = (1+2x)`, where x is the distance from its one end. Find the distance of its center of mass from this end.

Explanation

To find the distance of the center of mass from one end of a thin rod with a linear density given by \(\lambda = 1 + 2x\), where \(x\) is the distance from one end, we can follow these steps:

### Step 1: Understand the Problem
We have a thin rod of length \(L = 1 \, \text{m}\) and a linear density \(\lambda(x) = 1 + 2x\). We need to find the center of mass of this rod.

### Step 2: Define the Mass Element
The mass element \(dm\) of a small segment of the rod of length \(dx\) at position \(x\) can be expressed as:
\[
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