Question

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

• A. $2\text{sq. units}$
• B. $4\text{sq. units}$
• C. $3\text{sq. units}$
• D. $1\text{sq. units}$

Answer 1

The correct option is A $2\text{sq. units}$


As area is always positive, therefore we will take positive sign of $cosx$ in $[0,\frac{\pi }{2}]$ and negative sign in $[\frac{\pi }{2},\pi ]$
From the figure,
$A=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\cos xdx-\underset{\frac{\pi }{2}}{\overset{\pi }{\int }}\cos xdx$

$=[\sin x{]}_0^{\frac{\pi }{2}}-[\sin x{]}_{\frac{\pi }{2}}^{\pi }$

$=2\text{sq. units}$