A) \[3\pi /4\]
B) \[\pi /4\]
C) \[\pi /8\]
D) \[\pi /2\]
Correct Answer: C
Solution :
\[I=\frac{1}{2}\int\limits_{0}^{\pi /2}{x|\cos 2x|dx;2x=t\Rightarrow dx=\frac{dt}{2}}\] \[I=\frac{1}{8}\int\limits_{0}^{\pi }{t|\cos t|dt}\] \[I=\frac{1}{8}\int\limits_{0}^{\pi }{(\pi -t)|\cot |dt}\] \[2I=\frac{1}{8}\int\limits_{0}^{\pi }{|\cos t|dt}=\frac{2\pi }{8}\Rightarrow I=\frac{\pi }{8}\]You need to login to perform this action.
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