Question

The value of \( \int_{1}^{4} |x - 3| \, dx \) is equal to

• A. 2
• B. \( \frac{5}{2} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{3}{2} \)

Hint:

For integrals involving absolute values, split the integral at the point where the expression inside the absolute value changes sign.

Answer 1

The Correct Option is B

Step 1: Split the integral.
Since the absolute value function changes sign at \( x = 3 \), split the integral into two parts: one from 1 to 3, and another from 3 to 4, then integrate each part separately.

Step 2: Conclusion.
Thus, the correct answer is option (B).

Final Answer: \[ \boxed{\text{(B) } \frac{5}{2}} \]