question_answer

\[\int_{0}^{10\pi }{|\sin x|}\,\,dx\]is:

A) \[20\]                                   

B) \[8\]

C) \[10\]                                   

D) \[18\]

Correct Answer: A

Solution :

Key Idea: The period of \[|\sin x|\] is\[n\].                 \[\int_{0}^{10\pi }{|\sin x|}\,\,dx\]                 \[=\left[ \int_{0}^{\pi /2}{\sin x\,\,dx+\int_{\pi /2}^{\pi }{\sin x}\,\,dx} \right]\]                 \[=10[-\cos x]_{0}^{\pi /2}+[-\cos x]_{\pi /2}^{\pi }\] Alternative Solution: \[\therefore \]Required area                 \[=10\int_{0}^{\pi }{\sin x}\,\,dx\] \[=10[-\cos x]_{0}^{\pi }=-10(\cos \pi -\cos 0)=20\]