By using the properties of definite integrals, evaluate the integrals`int_2^ 8|x-5|dx` and `int_-5^5|x+2|dx`

Explanation

To evaluate the integrals \( \int_2^8 |x-5| \, dx \) and \( \int_{-5}^5 |x+2| \, dx \) using properties of definite integrals, we will break down the steps as follows:

### Step 1: Evaluate \( \int_2^8 |x-5| \, dx \)

1. **Identify the point where the expression inside the absolute value changes sign**:
- The expression \( |x-5| \) changes at \( x = 5 \).
- For \( x < 5 \), \( |x-5| = -(x-5) = 5-x \).
- For \( x \geq 5 \), \( |x-5| = x-5 \).
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