A) \[2+\sqrt{2}\]
B) \[2-\sqrt{2}\]
C) \[-2+\sqrt{2}\]
D) 0
Correct Answer: B
Solution :
Let \[I=\int_{0}^{\pi /2}{\left| \sin \left( x-\frac{\pi }{4} \right)\, \right|}\,dx\] \[x-\frac{\pi }{4}\]is ?ve when \[x\le \frac{\pi }{4}\]and +ve when \[x>\frac{\pi }{4}\] \[=-\int_{0}^{\pi /4}{\sin \left( x-\frac{\pi }{4} \right)dx+\int_{\pi /4}^{\pi /2}{\sin \left( x-\frac{\pi }{4} \right)dx}}\]\[=2-\sqrt{2}\].
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