The area enclosed by the curves \( y=\sin x+\cos x \) and P \( y=|\...

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The area enclosed by the curves \( y=\sin x+\cos x \) and
P \( y=|\cos x-\sin x| \) over the interval \( \left[0, \frac{\pi}{2}\right] \) is

W)
[JEE (Advanced) 2013]
(a) \( 4(\sqrt{2}-1) \)
(b) \( 2 \sqrt{2}(\sqrt{2}-1) \)
(c) \( 2(\sqrt{2}+1) \)
(d) \( 2 \sqrt{2}(\sqrt{2}+1) \)
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