Question

Area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is

• A. 2 sq units
• B. 4 sq units
• C. 3 sq units
• D. 1 sq unit

Answer 1

Answer: (A)

We have, $y=\cos x$ and lines $x=0,x=\pi$
Draw the rough sketch of the function $\cos x$.

$\therefore$ Required area $=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\cos xdx+\left|\underset{\frac{\pi }{2}}{\overset{\pi }{\int }}\cos xdx\right|$
$=[\sin x{]}_0^{\pi /2}+\left|[\sin x{]}_{\pi /2}^{\pi }\right|$
$=\left[\sin \frac{\pi }{2}-\sin 0\right]+\left|\left[\sin \pi -\sin \frac{\pi }{2}\right]\right|$
$=[1-0]+|0-1|$
$=1+1$
$=2$ sq units