A) 0
B) \[2(\sqrt{2}-1)\]
C) \[\sqrt{2}-1\]
D) \[2(\sqrt{2}+1)\]
Correct Answer: B
Solution :
\[\int_{0}^{\pi /2}{\,\,\,\,|\sin x-\cos x|dx}\] \[=\int_{0}^{\pi /4}{-(\sin x-\cos x})dx+\int_{\pi /4}^{\pi /2}{\,(\sin x-\cos x)dx}=2(\sqrt{2}-1)\].
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