Evaluate the following integral: `int_0^4(|x|+|x-2|+|x-4|)dx\ `

Explanation

To evaluate the integral \( I = \int_0^4 (|x| + |x-2| + |x-4|) \, dx \), we will break the integral into parts where the expressions inside the absolute values change.

### Step 1: Identify the points where the expressions change
The expressions \( |x| \), \( |x-2| \), and \( |x-4| \) change at \( x = 0 \), \( x = 2 \), and \( x = 4 \). Therefore, we will split the integral at these points.

### Step 2: Break the integral into intervals
We can break the integral into three parts:
1. From \( 0 \) to \( 2 \)
...