Question

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

• A. $0$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

The given curve is $y=\cos x.$

Clearly, $y\ge 0$ when $0\le x\le \frac{\pi }{2}$
$\therefore$ Required Area $=4\underset{0}{\overset{\pi /2}{\int }}ydx$
$=4\underset{0}{\overset{\pi /2}{\int }}\cos xdx=4[\sin x{]}_0^{\pi /2}$
$=4$ sq. units.