Question

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

• A. \(2\sqrt2\)
• B. \(2\sqrt2-2\)
• C. \(2\sqrt2+2\)
• D. 0

Hint:

For absolute value graphs, split the interval where the expression changes sign.

Answer 1

The Correct Option is B

Split at \(x = \frac{\pi}{4}\):
\[ \int_{0}^{\pi/4} (\cos x - \sin x) \, dx + \int_{\pi/4}^{\pi/2} (\sin x - \cos x) \, dx = 2(\sqrt{2} - 1) = 2\sqrt{2} - 2. \]