question_answer

The area bounded by the curve \[y=\left| \,\sin x\, \right|,\]\[x\text{-}\]axis and the lines \[\left| \,x\, \right|=\pi ,\]is

A)  2 sq unit

B)  1 sq unit

C)  4 sq unit

D)  None of these

Correct Answer: C

Solution :

Required area = Shaded area \[=\int_{-\pi }^{\pi }{\left| \sin x \right|dx=2\int_{0}^{\pi }{\left| \sin x \right|}}\,dx\] \[=-\,2[\cos x]_{0}^{\pi }\] \[=-(\cos \pi -\cos 0)\] \[\text{=}\,\,\text{4}\,\,\text{sq}\,\text{unit}\]