Question

Area between the curve y=cos x and x-axis when $0\le x\le 2\pi$ is

• A. 2
• B. 4
• C. 3

Answer 1

The correct option is B 4

$y=cosx$, When $xϵ[0,\frac{\pi }{2}],cosx\ge 0$
When $xϵ[\frac{\pi }{2},\frac{3\pi }{2}],cosx\le 0$
When $xϵ[\frac{3\pi }{2},2\pi ],cosx\ge 0$
Thus required area is given by,
${\int }_0^{\frac{\pi }{2}}ydx={\int }_0^{\frac{\pi }{2}}cosxdx+{\int }_{\frac{\pi }{2}}^{\frac{3\pi }{2}}(-cosx)dx+{\int }_{\frac{3\pi }{2}}^{2\pi }cosxdx$
$=1+2+1=4$ sq. unit