A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{8}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{3\pi }{4}\]
Correct Answer: B
Solution :
\[I=\frac{1}{2}\,\int\limits_{0}^{\pi /2}{x|\cos 2x|dx;\,\,2x=t\,\Rightarrow \,dx\,=\frac{dt}{2}}\] \[I=\frac{1}{8}\,\int\limits_{0}^{\pi }{t|\cos t|\,dt}\] \[I=\frac{1}{8}\int\limits_{0}^{\pi }{(\pi -t)\,|\cos t|\,dt}\] \[2I=\frac{\pi }{8}\,\int\limits_{0}^{\pi }{|\cos t|\,dt=\frac{2\pi }{8}}\] \[\Rightarrow \,\,1=\frac{\pi }{8}\]
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