Question

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

Answer 1

The correct option is B 4 sq. unit

We have $y=sinx$
$\begin{array}{ccccccc}x& 0& \frac{\pi }{6}& \frac{\pi }{2}& \pi & \frac{3\pi }{2}& 2\pi \\ y& 0& 0.5& 1& 0& -1& 0\end{array}$
Join these points with a free hand to obtain a rough sketch



Required area=(area of OAB)+(area of BCD)\\
$={\int }_0^{\pi }ydx+{\int }_{\pi }^{2\pi }(-y)dx$,
($\because$ Area BCD is below x - axis)\\
$=in{t}_0^{\pi }sinxdx-in{t}_{\pi }^{2\pi }sinxdx=4$ sq. unit.