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
The area under the curve \(y = |\cos x - \sin x|\), for \(0 \le x \le \frac{\pi}{2}\), and above the x-axis is
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For absolute value graphs, split the interval where the expression changes sign.
Updated On: Mar 23, 2026
- \(2\sqrt2\)
- \(2\sqrt2-2\)
- \(2\sqrt2+2\)
- 0
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The Correct Option is B
Solution and Explanation
Split at \(x = \frac{\pi}{4}\):
\[ \int_{0}^{\pi/4} (\cos x - \sin x) \, dx + \int_{\pi/4}^{\pi/2} (\sin x - \cos x) \, dx = 2(\sqrt{2} - 1) = 2\sqrt{2} - 2. \]
\[ \int_{0}^{\pi/4} (\cos x - \sin x) \, dx + \int_{\pi/4}^{\pi/2} (\sin x - \cos x) \, dx = 2(\sqrt{2} - 1) = 2\sqrt{2} - 2. \]
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