Question

The area under the curve \( y = | \cos x - \sin x | \), where \( 0 \leq x \leq \frac{\pi}{2} \), and the x-axis is:

• A. \( 2\sqrt{2} \)
• B. \( 2\sqrt{2} - 2 \)
• C. \( 2\sqrt{2} + 6y \)
• D. 0

Hint:

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

Answer 1

The Correct Option is B

The absolute value function requires breaking the integral into parts where \( \cos x \) and \( \sin x \) have different signs. The total area is calculated as \( 2\sqrt{2} - 2 \).
Final Answer: \[ \boxed{2\sqrt{2} - 2} \]