Question

Area bounded by the curve $y=\sin x$ and the $x$-axis between $x=0$ and $x=\pi$ is

• A. 2 sq. units
• B. 4 sq. units
• C. 8 sq. units
• D. None of these

Answer 1

The correct option is A 2 sq. units

We have the following table of values for $y=\sin x$
$$\begin{array}{ccccc}x& 0& \frac{\pi }{6}& \frac{\pi }{2}& \pi \\ y& 0& 0.5& 1& 0\end{array}$$
Join these points with a free hand to obtain a rough sketch.



Required area = area under $OAB$
$={\int }_0^{\pi }ydx$

$={\int }_0^{\pi }\sin xdx$
$=[-\cos x{]}_0^{\pi }$
$=-\cos \pi -(-\cos 0^{\circ })$
$=1+1$
$=2$sq. units