A) 2
B) 4
C) \[2\pi \]
D) \[4\pi \]
Correct Answer: A
Solution :
The curves \[y=x\]and \[y=x\] intersect at (0, 0) and \[(\pi ,\pi )\]. Hence area bounded by the two curves \[=\int\limits_{0}^{\pi }{(x+\sin x)dx-\int\limits_{0}^{\pi }{x\,dx}=\int\limits_{0}^{\pi }{\sin x\,dx}}\] \[=[-\cos x]_{0}^{\pi }=-\cos \pi +\cos 0=-(-1)+(1)=2\].
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