Question

Area of the region bounded by curve $y=\cos x$ between $x=0$ and $x=3\pi$ is ___________.

• A. $2$
• B. $6$
• C. $4$
• D. $3$

Answer 1

The correct option is B $6$

Area $A=\left|\stackrel{3\pi }{\underset{0}{\int }}\cos xdx\right|$
First we find area in first quadrant. Then to get total area as multiply it by $6$
$\therefore A=6\left|\stackrel{\pi /2}{\underset{0}{\int }}\cos xdx\right|$
$=6\left|\right(\sin x{)}_0^{\pi /2}|$
$=6|\sin \frac{\pi }{2}-\sin 0|$
$=6(1-0)$
$\therefore$ Total area $=6$ unit