`int_2^8|x-5|dx`

Explanation

To solve the integral \( \int_2^8 |x-5| \, dx \), we will follow these steps:

### Step 1: Determine where the expression inside the modulus changes sign
The expression \( |x-5| \) changes sign at \( x = 5 \). Therefore, we will break the integral into two parts: from 2 to 5 and from 5 to 8.

### Step 2: Rewrite the integral based on the intervals
For \( x < 5 \) (from 2 to 5), \( |x-5| = -(x-5) = 5-x \).
For \( x \geq 5 \) (from 5 to 8), \( |x-5| = x-5 \).
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