Question

The area bounded by the curve $y=\cos x,x$-axis between the ordinates $x=0,x=2\pi$ is:

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

Answer 1

Answer: (B)

$4$ sq. units

Given $y=\cos x$

Required Area$=\stackrel{2\pi }{\underset{0}{\int }}\cos xdx$

$=4\stackrel{\pi /2}{\underset{0}{\int }}\cos xdx$

$=4\sin x{|}_0^{\pi /2}=4[\sin \frac{\pi }{2}-\sin 0]$

$=4[1-0]$

$=4$ sq.units