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 = sin x
$\begin{array}{ccccccc}x& 0& \frac{\pi }{6}& \frac{\pi }{2}& \pi & \frac{3\pi }{2}& 2\pi \\ y& 0& 0.5& 1& 0& -1& 0\end{array}$
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)
$={\int }_0^{\pi }sinxdx-{\int }_{\pi }^{2\pi }sinxdx=4sq.unit$