Question

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

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

Answer 1

The correct option is D $2sq$. units

$y=\cos x,x=0$ and $x=\pi$ is shaded area
Area$={\int }_0^{\pi /2}ydx+{\int }_{\pi /2}^{\pi }ydx$
$={\int }_0^{\pi /2}(\cos x-0)dx+{\int }_{\pi /2}^{\pi }(0-\cos x)dx$
$={\int }_0^{\pi /2}\cos x-{\int }_{\pi /2}^{\pi }\cos xdx$
$={\left|\sin x\right|}_0^{\pi /2}-{\left|\sin x\right|}_{\pi /2}^{\pi }$
$=[1-0]-[0-1]$
$=2$ sq.units