By using the properties of definite integral, evaluate the integrals`int_2^ 8|x-5|dx`

Explanation

To evaluate the integral \( \int_2^8 |x - 5| \, dx \) using properties of definite integrals, we will break it down into two parts based on the definition of the absolute value function.

### Step-by-Step Solution:

1. **Identify the critical point**:
The expression inside the absolute value is \( x - 5 \). The critical point occurs when \( x - 5 = 0 \), which gives us \( x = 5 \). This point divides the integral into two intervals: from \( 2 \) to \( 5 \) and from \( 5 \) to \( 8 \).

2. **Break the integral into two parts**:
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