A) \[-\pi \]
B) \[\pi /2\]
C) \[\pi \]
D) \[2\pi \]
Correct Answer: C
Solution :
\[\int\limits_{-2\pi }^{7\pi }{\frac{\sin x}{|\sin x|}dx}\] \[\frac{\sin x}{|\sin x|}=\left\{ \begin{matrix} 1, & \sin x>0 \\ -1, & \sin x<0 \\ \end{matrix} \right.\] \[\Rightarrow \,\] \[\int\limits_{-2\pi }^{6\pi }{\frac{\sin x}{|\sin x|}}dx=0\] \[\Rightarrow \,\] \[\int\limits_{6\pi }^{7\pi }{\frac{\sin x}{|\sin x|}}dx=\pi \]
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