Find coordinates of mass center of a non-uniform rod of length L whose linear mass density lambda varies as lambda=a+bx, where x is the distance from the lighter end.

Explanation

To find the coordinates of the center of mass of a non-uniform rod of length \( L \) with a linear mass density given by \( \lambda = a + bx \), where \( x \) is the distance from the lighter end, we can follow these steps:

### Step 1: Define the mass element
The linear mass density is given as:
\[ \lambda(x) = a + bx \]
To find the mass element \( dm \) for a small segment \( dx \) of the rod, we can express it as:
...