question_answer

Area bounded by the curve \[y=\sin x\] between \[x=0\] and \[x=2\pi \] is

A)            2 sq. unit                                

B)            4 sq. unit

C)            8 sq. unit                                

D)            None of these

Correct Answer: B

Solution :

                   We have \[y=\sin x\]

\[x\]	0	\[\pi /6\]	\[\pi /2\]	\[\pi \]	\[3\pi /2\]	\[2\pi \]
\[y\]	0	0.5	1	0	?1	0

              Join these points with a free hand to obtain a rough sketch                               Required area = (area of \[OAB\]) + (area of\[BCD)\]                                          = \[\int_{0}^{\pi }{\,y\,dx+\int_{\pi }^{2\pi }{(-y)\,dx}}\],                                                    (\[\because \] Area \[BCD\] is below \[x-\]axis)                                                                          = \[\int_{0}^{\pi }{\sin x\,dx-\int_{\pi }^{2\pi }{\sin x\,dx=4}}\] sq. unit.